Nelson Functions 11
1st Edition
ISBN: 9780176332037
Textbook solutions
All Solutions
Page 212: Getting Started
Exercise 1
Step 1
1 of 7
a) $7^2=7times 7 =49$
$a^2=atimes a$
Step 2
2 of 7
b) $2^5=2times 2 times 2times 2times 2=32$
$a^5$ is $a$ multiplied by itself 5 times
Step 3
3 of 7
c) $5^{-1}=dfrac{1}{5}$
$$
a^{-m}=dfrac{1}{a^m}
$$
a^{-m}=dfrac{1}{a^m}
$$
Step 4
4 of 7
d) $10^0=1$
$a^0=1$ for all $aneq 0$
Step 5
5 of 7
e) $100^2=100times100=10,000$
$a^2=atimes a$
Step 6
6 of 7
f) $2^{-3}=dfrac{1}{2^3}=dfrac{1}{2times2times2}=dfrac{1}{8}$
$$
a^{-m}=dfrac{1}{a^m}
$$
a^{-m}=dfrac{1}{a^m}
$$
Result
7 of 7
a) 49
b) 32
c) $dfrac{1}{5}$
d) $1$
e) 10,000
f) $dfrac{1}{8}$
Exercise 2
Step 1
1 of 3
Rule of exponent: If the base is negative, an even exponent will result in positive number while an odd exponent will result in negative number.
Step 2
2 of 3
a) $(-3)^2=(-3)times(-3)=9$
b) $(-3)^3=(-3)times(-3)times(-3)=-27$
c) $-4^2=-4times4=-16$
d) $(-4)^2=(-4)times(-4)=16$
e) $(-5)^3=(-5)times(-5)times(-5)=-125$
f) $-5^3=-5times 5 times 5=-125$
Result
3 of 3
a) 9
b) $-27$
c) $-16$
d) $16$
e) $-125$
f) $-125$
Exercise 3
Step 1
1 of 2
$(-a)^m$ is always positive if $m$ is even while it is negative if $m$ is odd.
In this case, $(-5)^{120}$, the exponent is even, so it is positive.
Result
2 of 2
positive
Exercise 4
Step 1
1 of 3
Remember that $(a^m)^n=a^{mn}$
Step 2
2 of 3
a) $(3^2)^2=3^4=3times3times3times3=81$
b) $(7^2)^4=7times7times7times7times7=2401$
c) $[(-4)^2]^3=[(-4)^2]^3=16^3=16times16times16=4096$
d) $[-(10^2)]^3=[-100]^3=(-100)(-100)(-100)=-1,000,000$
e) $[(2^2)^2]=(4^2)=4times4=16$
f) $-[(2^2)^2]^0=-(4^2)^0=-1$
Result
3 of 3
a) $81$
b) $2401$
c) $4096$
d) $-1,000,000$
e) $16$
f) $-1$
Exercise 5
Step 1
1 of 2
Remember the rule of exponents
$$
sqrt{a^2}=a
$$
$sqrt{a^2cdot b}=asqrt{b}$
a) $(sqrt{49})^2=49$
b) $(3sqrt{64})=3sqrt{8^2}=3times 8 = 24$
c) $sqrt{4}timessqrt{16}=2times 4=8$
d) $dfrac{sqrt{9}}{sqrt{81}}=sqrt{dfrac{9}{81}}=sqrt{dfrac{1}{9}}=dfrac{1}{sqrt{9}}=dfrac{1}{sqrt{3^2}}=dfrac{1}{3}$
Result
2 of 2
a) 49
b) 24
c) 8
d) $dfrac{1}{3}$
Exercise 6
Step 1
1 of 7
[begin{gathered}
{text{In this exercise we shall evaluate the following:}} hfill \
{text{a) To find the sum of the fractions, find first their LCD}}{text{.}} hfill \
{text{The LCD of }}frac{5}{8}{text{ and }}frac{5}{3}{text{ is 24}}{text{.}} hfill \
{text{Change the fractions to similar one}}{text{.}} hfill \
frac{5}{8} + frac{5}{3} = frac{{left( {24 div 8} right)left( 5 right)}}{{24}} + frac{{left( {24 div 3} right)left( 5 right)}}{{24}} hfill \
{text{Hence,}} hfill \
{text{ = }}frac{{15}}{{24}} + frac{{40}}{{24}} hfill \
{text{Add the numerator and place the sum over the denaminator}}{text{.}} hfill \
frac{5}{8} + frac{5}{3} = frac{{55}}{{24}} hfill \
end{gathered} ]
{text{In this exercise we shall evaluate the following:}} hfill \
{text{a) To find the sum of the fractions, find first their LCD}}{text{.}} hfill \
{text{The LCD of }}frac{5}{8}{text{ and }}frac{5}{3}{text{ is 24}}{text{.}} hfill \
{text{Change the fractions to similar one}}{text{.}} hfill \
frac{5}{8} + frac{5}{3} = frac{{left( {24 div 8} right)left( 5 right)}}{{24}} + frac{{left( {24 div 3} right)left( 5 right)}}{{24}} hfill \
{text{Hence,}} hfill \
{text{ = }}frac{{15}}{{24}} + frac{{40}}{{24}} hfill \
{text{Add the numerator and place the sum over the denaminator}}{text{.}} hfill \
frac{5}{8} + frac{5}{3} = frac{{55}}{{24}} hfill \
end{gathered} ]
Step 2
2 of 7
[begin{gathered}
{text{b)To find the difference of the fractions, find first their LCD}}{text{.}} hfill \
{text{The LCD of }}frac{5}{8}{text{ and }}frac{5}{3}{text{ is 24}}{text{.}} hfill \
{text{Change the fractions to similar one}}{text{.}} hfill \
frac{5}{8} – frac{5}{3} = frac{{left( {24 div 8} right)left( 5 right)}}{{24}} – frac{{left( {24 div 3} right)left( 5 right)}}{{24}} hfill \
{text{Hence,}} hfill \
{text{ = }}frac{{15}}{{24}} – frac{{40}}{{24}} hfill \
{text{Subtract the numerator and place the difference over the denaminator}}{text{.}} hfill \
frac{5}{8} – frac{5}{3} = – frac{{25}}{{24}} hfill \
end{gathered} ]
{text{b)To find the difference of the fractions, find first their LCD}}{text{.}} hfill \
{text{The LCD of }}frac{5}{8}{text{ and }}frac{5}{3}{text{ is 24}}{text{.}} hfill \
{text{Change the fractions to similar one}}{text{.}} hfill \
frac{5}{8} – frac{5}{3} = frac{{left( {24 div 8} right)left( 5 right)}}{{24}} – frac{{left( {24 div 3} right)left( 5 right)}}{{24}} hfill \
{text{Hence,}} hfill \
{text{ = }}frac{{15}}{{24}} – frac{{40}}{{24}} hfill \
{text{Subtract the numerator and place the difference over the denaminator}}{text{.}} hfill \
frac{5}{8} – frac{5}{3} = – frac{{25}}{{24}} hfill \
end{gathered} ]
Step 3
3 of 7
[begin{gathered}
{text{c) To find the quotient of the fractions, get the reciprocal }} hfill \
{text{of the second fraction}}{text{. }} hfill \
frac{7}{8} div frac{2}{3} = frac{7}{8} cdot frac{3}{2} hfill \
{text{Multiply the first fraction by the reciprocal}}{text{.}} hfill \
frac{7}{8} cdot frac{3}{2} = frac{{left( 7 right)left( 3 right)}}{{left( 8 right)left( 2 right)}} hfill \
{text{Hence,}} hfill \
frac{7}{8} div frac{2}{3} = frac{{21}}{{16}} hfill \
end{gathered} ]
{text{c) To find the quotient of the fractions, get the reciprocal }} hfill \
{text{of the second fraction}}{text{. }} hfill \
frac{7}{8} div frac{2}{3} = frac{7}{8} cdot frac{3}{2} hfill \
{text{Multiply the first fraction by the reciprocal}}{text{.}} hfill \
frac{7}{8} cdot frac{3}{2} = frac{{left( 7 right)left( 3 right)}}{{left( 8 right)left( 2 right)}} hfill \
{text{Hence,}} hfill \
frac{7}{8} div frac{2}{3} = frac{{21}}{{16}} hfill \
end{gathered} ]
Step 4
4 of 7
[begin{gathered}
{text{d) Find first the product of the fractions}}{text{.}} hfill \
frac{1}{5} – frac{3}{8}left( {frac{4}{3}} right) hfill \
{text{Get the factor of both numerators and denaminators}}{text{.}} hfill \
= frac{1}{5} – frac{3}{{4 times 2}}left( {frac{4}{3}} right) hfill \
= frac{1}{5} – frac{3}{{4 times 2}}left( {frac{4}{3}} right) hfill \
= frac{1}{5} – frac{{cancel{3}}}{{cancel{4} times 2}}left( {frac{{cancel{4}}}{{cancel{3}}}} right) hfill \
{text{Hence,}} hfill \
= frac{1}{5} – frac{1}{2} hfill \
{text{Find their common denaminator}}{text{.}} hfill \
= frac{1}{5} – frac{1}{2} = frac{{(2)(1)}}{{10}} – frac{{(5)(1)}}{{10}} hfill \
{text{Subtract the factors and place the difference over the denaminator}}{text{.}} hfill \
= frac{2}{{10}} – frac{5}{{10}} = – frac{3}{{10}} hfill \
end{gathered} ]
{text{d) Find first the product of the fractions}}{text{.}} hfill \
frac{1}{5} – frac{3}{8}left( {frac{4}{3}} right) hfill \
{text{Get the factor of both numerators and denaminators}}{text{.}} hfill \
= frac{1}{5} – frac{3}{{4 times 2}}left( {frac{4}{3}} right) hfill \
= frac{1}{5} – frac{3}{{4 times 2}}left( {frac{4}{3}} right) hfill \
= frac{1}{5} – frac{{cancel{3}}}{{cancel{4} times 2}}left( {frac{{cancel{4}}}{{cancel{3}}}} right) hfill \
{text{Hence,}} hfill \
= frac{1}{5} – frac{1}{2} hfill \
{text{Find their common denaminator}}{text{.}} hfill \
= frac{1}{5} – frac{1}{2} = frac{{(2)(1)}}{{10}} – frac{{(5)(1)}}{{10}} hfill \
{text{Subtract the factors and place the difference over the denaminator}}{text{.}} hfill \
= frac{2}{{10}} – frac{5}{{10}} = – frac{3}{{10}} hfill \
end{gathered} ]
Step 5
5 of 7
[begin{gathered}
{text{e) Find first the quotient of the fractions}}{text{.}} hfill \
= – frac{4}{3}left( {frac{9}{{10}} div frac{5}{{12}}} right) hfill \
{text{Get the reciprocal of the third fraction}}{text{. }} hfill \
= – frac{4}{3}left( {frac{9}{{10}} cdot frac{{12}}{5}} right) hfill \
{text{Get the factor of both numerators and denaminators}}{text{.}} hfill \
= – frac{4}{3} + left( {frac{9}{{10}} cdot frac{{12}}{5}} right) = – frac{4}{3} + left( {frac{9}{{left( 5 right)left( {cancel{2}} right)}} cdot frac{{left( 6 right)left( {cancel{2}} right)}}{5}} right) hfill \
{text{Hence,}} hfill \
= – frac{4}{3} + left( {frac{{36}}{{25}}} right) hfill \
{text{Multiply the fractions}}{text{. }} hfill \
{text{Get their common denaminator and multiply}}{text{.}} hfill \
= – frac{4}{3} cdot frac{{54}}{{25}} = frac{{100}}{{75}} cdot frac{{162}}{{75}} = frac{{62}}{{75}} hfill \
{text{Hence,}} hfill \
= – frac{4}{3} + left( {frac{9}{{10}} cdot frac{{12}}{5}} right) = frac{{62}}{{75}} hfill \
end{gathered} ]
{text{e) Find first the quotient of the fractions}}{text{.}} hfill \
= – frac{4}{3}left( {frac{9}{{10}} div frac{5}{{12}}} right) hfill \
{text{Get the reciprocal of the third fraction}}{text{. }} hfill \
= – frac{4}{3}left( {frac{9}{{10}} cdot frac{{12}}{5}} right) hfill \
{text{Get the factor of both numerators and denaminators}}{text{.}} hfill \
= – frac{4}{3} + left( {frac{9}{{10}} cdot frac{{12}}{5}} right) = – frac{4}{3} + left( {frac{9}{{left( 5 right)left( {cancel{2}} right)}} cdot frac{{left( 6 right)left( {cancel{2}} right)}}{5}} right) hfill \
{text{Hence,}} hfill \
= – frac{4}{3} + left( {frac{{36}}{{25}}} right) hfill \
{text{Multiply the fractions}}{text{. }} hfill \
{text{Get their common denaminator and multiply}}{text{.}} hfill \
= – frac{4}{3} cdot frac{{54}}{{25}} = frac{{100}}{{75}} cdot frac{{162}}{{75}} = frac{{62}}{{75}} hfill \
{text{Hence,}} hfill \
= – frac{4}{3} + left( {frac{9}{{10}} cdot frac{{12}}{5}} right) = frac{{62}}{{75}} hfill \
end{gathered} ]
Step 6
6 of 7
[begin{gathered}
{text{f) Find first the sum of the fractions}}{text{.}} hfill \
– frac{9}{{10}}left( {frac{3}{8} + frac{7}{3}} right) hfill \
{text{Get their LCD and add}}{text{.}} hfill \
= – frac{9}{{10}}left( {frac{3}{8} + frac{7}{3}} right) = – frac{9}{{10}}left( {frac{9}{{24}} + frac{{56}}{{24}}} right) hfill \
= – frac{9}{{10}}left( {frac{{65}}{{24}}} right) hfill \
{text{Get the factor of both numerators and denaminators}}{text{.}} hfill \
= – frac{9}{{10}} cdot frac{{65}}{{24}} = frac{{left( {cancel{3}} right)left( 3 right)}}{{left( {cancel{5}} right)left( 2 right)}} cdot frac{{left( {cancel{5}} right)left( {13} right)}}{{left( {cancel{3}} right)left( 8 right)}} hfill \
{text{Multiply}}{text{.}} hfill \
= frac{3}{2} cdot frac{{13}}{8} = frac{{39}}{{16}} hfill \
end{gathered} ]
{text{f) Find first the sum of the fractions}}{text{.}} hfill \
– frac{9}{{10}}left( {frac{3}{8} + frac{7}{3}} right) hfill \
{text{Get their LCD and add}}{text{.}} hfill \
= – frac{9}{{10}}left( {frac{3}{8} + frac{7}{3}} right) = – frac{9}{{10}}left( {frac{9}{{24}} + frac{{56}}{{24}}} right) hfill \
= – frac{9}{{10}}left( {frac{{65}}{{24}}} right) hfill \
{text{Get the factor of both numerators and denaminators}}{text{.}} hfill \
= – frac{9}{{10}} cdot frac{{65}}{{24}} = frac{{left( {cancel{3}} right)left( 3 right)}}{{left( {cancel{5}} right)left( 2 right)}} cdot frac{{left( {cancel{5}} right)left( {13} right)}}{{left( {cancel{3}} right)left( 8 right)}} hfill \
{text{Multiply}}{text{.}} hfill \
= frac{3}{2} cdot frac{{13}}{8} = frac{{39}}{{16}} hfill \
end{gathered} ]
Result
7 of 7
a) $dfrac{55}{24}$ $;;;;$ b) $-dfrac{25}{24}$ $;;;;$ c) $dfrac{21}{16}$
d) $-dfrac{3}{10}$ $;;;;$ e) $dfrac{62}{75}$ $;;;;$ f) $-dfrac{39}{16}$
Exercise 7
Step 1
1 of 5
[begin{gathered}
{text{In this exercise we shall simplify the following:}} hfill \
{text{a) Remember this rule, }}{a^n}left( {{a^m}} right) = {a^{n + m}} hfill \
{a^2}left( {{a^5}} right) = {a^{2 + 5}} hfill \
{text{Hence,}} hfill \
{a^2}left( {{a^5}} right) = {a^7} hfill \
end{gathered} ]
{text{In this exercise we shall simplify the following:}} hfill \
{text{a) Remember this rule, }}{a^n}left( {{a^m}} right) = {a^{n + m}} hfill \
{a^2}left( {{a^5}} right) = {a^{2 + 5}} hfill \
{text{Hence,}} hfill \
{a^2}left( {{a^5}} right) = {a^7} hfill \
end{gathered} ]
Step 2
2 of 5
[begin{gathered}
{text{b) Remember this rule, }}{{text{a}}^n} div {a^m} = {a^{n – m}} hfill \
{b^{12}} div {b^8} = {b^{12 – 8}} hfill \
{text{Hence,}} hfill \
{b^{12}} div {b^8} = {b^4} hfill \
end{gathered} ]
{text{b) Remember this rule, }}{{text{a}}^n} div {a^m} = {a^{n – m}} hfill \
{b^{12}} div {b^8} = {b^{12 – 8}} hfill \
{text{Hence,}} hfill \
{b^{12}} div {b^8} = {b^4} hfill \
end{gathered} ]
Step 3
3 of 5
[begin{gathered}
{text{c) Remember this rule, (}}{a^n}{)^m} = {a^{n cdot m}} hfill \
{left( {{c^3}} right)^4} = {c^{3 cdot 4}} hfill \
{text{Hence,}} hfill \
{left( {{c^3}} right)^4} = {c^{12}} hfill \
end{gathered} ]
{text{c) Remember this rule, (}}{a^n}{)^m} = {a^{n cdot m}} hfill \
{left( {{c^3}} right)^4} = {c^{3 cdot 4}} hfill \
{text{Hence,}} hfill \
{left( {{c^3}} right)^4} = {c^{12}} hfill \
end{gathered} ]
Step 4
4 of 5
[begin{gathered}
{text{d)Remember this rule, }} hfill \
{left( {{a^n}} right)^m} = {a^{n + m}} hfill \
{text{It follows that}} hfill \
d cdot {d^6} cdot {d^3} = {d^{1 + 6 + 3}} hfill \
{text{Hence,}} hfill \
dleft( {{d^6}} right){d^3} = {d^{10}} hfill \
end{gathered} ]
{text{d)Remember this rule, }} hfill \
{left( {{a^n}} right)^m} = {a^{n + m}} hfill \
{text{It follows that}} hfill \
d cdot {d^6} cdot {d^3} = {d^{1 + 6 + 3}} hfill \
{text{Hence,}} hfill \
dleft( {{d^6}} right){d^3} = {d^{10}} hfill \
end{gathered} ]
Result
5 of 5
a) $a^7$
b) $b^4$
c) $c^{12}$
d) $d^{10}$
Exercise 8
Step 1
1 of 2
[begin{gathered}
{text{In this excercise we shall determine the exponent that makes each eqaution true}}{text{.}} hfill \
{text{a) Factor such that both sides have the same base}}{text{.}} hfill \
{{text{9}}^x} = 81 hfill \
{9^x} = {9^2} hfill \
{text{Equate the exponents}}{text{.}} hfill \
x = 2 hfill \
hfill \
{text{b) Factor such that both sides have the same base}}{text{.}} hfill \
{8^m} = 256 hfill \
{2^{3m}} = {2^8} hfill \
3m = 8 hfill \
{text{Divide both sides of the equation by 3}}{text{.}} hfill \
m = frac{8}{3} hfill \
hfill \
{text{c) Factor such that both sides have the same base}}{text{.}} hfill \
{( – 5)^a} = – 125 hfill \
{( – 5)^a} = – {5^3} hfill \
{text{Equate the exponents}}{text{.}} hfill \
a = 3 hfill \
hfill \
{text{d) Factor such that both sides have the same base}}{text{.}} hfill \
– {10^r} = – 100,000,000 hfill \
– {10^r} = – {10^8} hfill \
{text{Equate the exponents}}{text{.}} hfill \
r = 8 hfill \
end{gathered} ]
{text{In this excercise we shall determine the exponent that makes each eqaution true}}{text{.}} hfill \
{text{a) Factor such that both sides have the same base}}{text{.}} hfill \
{{text{9}}^x} = 81 hfill \
{9^x} = {9^2} hfill \
{text{Equate the exponents}}{text{.}} hfill \
x = 2 hfill \
hfill \
{text{b) Factor such that both sides have the same base}}{text{.}} hfill \
{8^m} = 256 hfill \
{2^{3m}} = {2^8} hfill \
3m = 8 hfill \
{text{Divide both sides of the equation by 3}}{text{.}} hfill \
m = frac{8}{3} hfill \
hfill \
{text{c) Factor such that both sides have the same base}}{text{.}} hfill \
{( – 5)^a} = – 125 hfill \
{( – 5)^a} = – {5^3} hfill \
{text{Equate the exponents}}{text{.}} hfill \
a = 3 hfill \
hfill \
{text{d) Factor such that both sides have the same base}}{text{.}} hfill \
– {10^r} = – 100,000,000 hfill \
– {10^r} = – {10^8} hfill \
{text{Equate the exponents}}{text{.}} hfill \
r = 8 hfill \
end{gathered} ]
Result
2 of 2
a) $x=2$
b) $m=dfrac{8}{3}$
c) $a=3$
d) $r=8$
Exercise 9
Step 1
1 of 2
[begin{gathered}
{text{In this excercise we shall evalaute the following}} hfill \
{text{formulas for }}r = 2.5{text{ cm and }}h = 4.8{text{ cm}} hfill \
hfill \
{text{a) Substitute }}2.5{text{cm for }}r{text{ and }}4.8{text{ for }}h hfill \
V = pi {left( {2.5} right)^2}left( {4.8} right) hfill \
V = pi left( {6.25} right)left( {4.8} right) hfill \
{text{Multiply}}{text{.}} hfill \
V = pi (30) hfill \
V = 3.14(30) hfill \
V = 94.248{text{c}}{{text{m}}^2} hfill \
hfill \
{text{b) Substitute }}2.5{text{cm for }}r hfill \
V = frac{4}{3}pi {left( {2.5} right)^3} hfill \
V = frac{4}{3}pi left( {15.625} right) hfill \
{text{Multiply}} hfill \
V = 65.45{text{c}}{{text{m}}^3} hfill \
end{gathered} ]
{text{In this excercise we shall evalaute the following}} hfill \
{text{formulas for }}r = 2.5{text{ cm and }}h = 4.8{text{ cm}} hfill \
hfill \
{text{a) Substitute }}2.5{text{cm for }}r{text{ and }}4.8{text{ for }}h hfill \
V = pi {left( {2.5} right)^2}left( {4.8} right) hfill \
V = pi left( {6.25} right)left( {4.8} right) hfill \
{text{Multiply}}{text{.}} hfill \
V = pi (30) hfill \
V = 3.14(30) hfill \
V = 94.248{text{c}}{{text{m}}^2} hfill \
hfill \
{text{b) Substitute }}2.5{text{cm for }}r hfill \
V = frac{4}{3}pi {left( {2.5} right)^3} hfill \
V = frac{4}{3}pi left( {15.625} right) hfill \
{text{Multiply}} hfill \
V = 65.45{text{c}}{{text{m}}^3} hfill \
end{gathered} ]
Result
2 of 2
a) $V=94.248;text{cm}^3$
b) $V=65.45;text{cm}^3$
Exercise 10
Step 1
1 of 4
To determine whether a function is linear or quadratic from a table of values, find the first differences and second differences. If the first differences are constant, it is linear. If the second differences are constant, it is quadratic.
Step 2
2 of 4
begin{table}[]
defarraystretch{1.5}%
begin{tabular}{|c|c|c|c|}
hline
$x$ & $y$ & First Differences & Second Differences \ hline
$-4$ & 12 & & \ hline
$-2$ & 7 & $7-12=-5$ & \ hline
0 & 2 & $2-7=-5$ & $0$ \ hline
2 & $-3$ & $-3-2=-5$ & $0$ \ hline
4 & $-8$ & $-8-(-3)=-5$ & $0$ \ hline
6 & $-13$ & $-13-(-8)=-5$ & $0$ \ hline
end{tabular}
end{table}
$bold{a);;} $ Since the first differences are constant and second differences are equal to zero, then it is linear.
defarraystretch{1.5}%
begin{tabular}{|c|c|c|c|}
hline
$x$ & $y$ & First Differences & Second Differences \ hline
$-4$ & 12 & & \ hline
$-2$ & 7 & $7-12=-5$ & \ hline
0 & 2 & $2-7=-5$ & $0$ \ hline
2 & $-3$ & $-3-2=-5$ & $0$ \ hline
4 & $-8$ & $-8-(-3)=-5$ & $0$ \ hline
6 & $-13$ & $-13-(-8)=-5$ & $0$ \ hline
end{tabular}
end{table}
$bold{a);;} $ Since the first differences are constant and second differences are equal to zero, then it is linear.
Step 3
3 of 4
begin{table}[]
defarraystretch{1.5}%
begin{tabular}{|c|c|c|c|}
hline
$x$ & $y$ & First Differences & Second Differences \ hline
$-3$ & $9$ & & \ hline
$-2$ & $10$ & $10-9=1$ & \ hline
$-1$ & $12$ & $12-10=2$ & $2-1=1$ \ hline
$0$ & $15$ & $15-12=3$ & $3-2=1$ \ hline
$1$ & $19$ & $19-15=4$ & $4-3=1$ \ hline
$2$ & $24$ & $24-19=5$ & $5-4=1$ \ hline
end{tabular}
end{table}
defarraystretch{1.5}%
begin{tabular}{|c|c|c|c|}
hline
$x$ & $y$ & First Differences & Second Differences \ hline
$-3$ & $9$ & & \ hline
$-2$ & $10$ & $10-9=1$ & \ hline
$-1$ & $12$ & $12-10=2$ & $2-1=1$ \ hline
$0$ & $15$ & $15-12=3$ & $3-2=1$ \ hline
$1$ & $19$ & $19-15=4$ & $4-3=1$ \ hline
$2$ & $24$ & $24-19=5$ & $5-4=1$ \ hline
end{tabular}
end{table}
$bold{b);;}$ Since the second differences are constant, then it is quadratic.
Result
4 of 4
a) linear
b) quadratic
unlock