College Algebra. Test 2: Graphs the Function – Flashcards

A) what transformation produces graph g from f? = because it is +3, you shift 3 units to the left.B) what transformations produces graph h from f? = because it is -4, you shift 4 units to the right.

1. first find the basic function in the equation, which is f(x)=√x 2. in comparison to f(x), 2f(x) is a vertical stretching of the graph of f(x) by a 2 units. 3. the value 3 in the equation is the y-value. therefore, you shift the graph up by 3 units.

1. start with the graph of the basic function in the equation, which is y=√x. 2. compare y=√x and y=√(x-7)... the difference is that the second one with a -7. 3.this means it is the same graph, but with a horizontal shift of 7 units to the right.

the answer is y=√-x +1 because if you reflect a function across the y-axis, its x values will be negative.

1. starting with f(x)=x³, shift 2 units left, to shift left the sign must be positive. so the equation is now f(x)=(x+2)³2.starting with f(x)=(x+2)³, stretch vertically by 3, this number always goes in the front of the equation. so now the equation is f(x)=3(x+2)³ 3. starting with f(x)=3(x+2)³, reflect about the y-axis. when you reflect about the y-axis the x values become negative. so the equation is now f(x)= 3(-x+2)³ 4. starting with f(x)= 3(-x+2)³, shift up by 6 units, this always goes at the end of the equation & if you are shifting up the sign has to be a +. so the final equation is= g(x)= 3(-x+2)³+6

1. first find points on the graph of f and write them down: (0,0) 2. next, transform the graph by the differences in the equation of g. shift vertically by 2 units.

what is the function that describes the new salary? p(x)= 1.04(f(x)+500)

to solve this problem simply plug in the equations of f and g into the formulas: a. f(-4) + g(-4) =-10b. f(0) - g(0) =-1 c. f(-1) * g(-1) =-1 d. f(2) / g(2) =1/(7√7)

to solve this problem first plug in the equations of f and g into the formulas: a. (f+g)(x) --> 5x+6+3x² because the equations for f and g do NOT involve division or contain even roots, the domain is the set of all real #'s: (-∞,∞) b.(f-g)(x) --> 5x+6-3x² domain: (-∞,∞) c. (f*g)(x) --> 15x³+18x² domain: (-∞,∞) d. (f/g)(x) --> (5x+6)/(3x²) domain: all real #'s excluding values of x for which the denominator=0. 0 is the only value to make 3x²=0, so we only exclude 0. = (-∞,0)∪(0,∞)

to solve this problem plug the equation of f into g, solve f as far as you can, then solve g: a) (g°f)(x) --> g(f(x)) =g(x²-2) =4(x²-2)+11 =4x²-8+11 =4x²+3

=3(-d)²-7 =g=3d²-7 =4(3d²-7)+5 =12d²-28+5 =12d²-23

(f°f)(3)= =7(3)-5 =21-5 =16 then plug in 16 into f: =7(16)-5 =112-5 =107

-first find (f°g)(x): =3/((5/x)+1)* x/x =3x/x+5-next determine domain of (f°g): g(x)= all real #'s except for 0 (f°g)(x)= all real #'s except -5 therefore, (-∞,-5)∪(-5,0)∪(0,∞)

a. (R-C)(11,000) R(x)=70(11,000) C(x)=550,000+45(11,000) =770,000-1045000 =-275,000 If the company sells 11,000 R in 1 year, its net loss is $275,000.b. (R-C)(22,000) R(x)=70(22,000) C(x)=550,000+45(22,000) =1,540,000-1,540,000 =0 The company doesn't make or lose any $. c.(R-C)(33,000) R(x)=70(33,000) C(x)=550,000+45(33,000) =2,310,000-2,035,000 =275,000 the company's net profit is $275,000.

solve this by drawing a horizontal line through the given graph, if it doesn't intersect the function more than once, it is one to one.

f⁻¹(4)=-2

a. f(-2)=(-2)³-5 =-8-5 =-13b. f⁻¹(-13)=-2 c. (f°f⁻¹)(353)=353

Find the points that are on the graph of the original function that is given. If the point (a,b) is on the graph of f, then the point (b,a) is in it's place on the graph f⁻¹. Example: graph of f: (0,-2), (2,-4), (3,2) graph of f⁻¹: (-2,0), (-4,2), (2,3)

To solve a), first write the original function w/t y, then swap the places of the x's and the y's, and solve for y. a) f(x)=6x+4 y=6x+4 x=6y+4 6y=x-4 y=(x-4)/6To solve b), -find the domain of f, this also is the answer for the range of the inverse function f⁻¹. -next, find the domain for f⁻¹, this is also the answer for the range of the function f. To solve c), pick a random set of points for each function and plot them on a graph, pick the graph that matches.

First write the original function w/t y, then swap the places of the x's and the y's, and solve for y: f(x)= x²+3, x≤0 y=x²+3, x≤0 x=y²+3, y≤0 x-3=y², y≤0 y=±√(x-3), y≤0 since y≤0, choose y=-√(x-3) therefore, f⁻¹=-√(x-3), x≥3(cant have √-#)- To make a graph, pick a random set of points for f and f⁻¹ and plot them on a graph, pick the graph that matches.

you have to ask the following questions: 1. does it have horizontal shift? - yes, right by 1 unit (-1) 2. does it shrink or stretch? -it stretches vertically by 4 units(4) 3. is it reflected? -yes,reflected by the x-axis (- at the beginning) 4.does it have vertical shift? - yes, down by 5 units. (-5)

a) the min or max value is determined by k - first you need to label your equation with a,b,and c. f(x)=2x²-20x+43 a b c-next, find h. h= -b/2a h=20/2(2) h=20/4 h=5 -now, find k. k=f(h)=2(5)²-20(5)+43 k=2(25)-100+43 k=50-143 k=-7 therefore, -7 is your minimum value. b) to find the range of f, (range=y values) the minimum is k=-7; k is the y value (h,k) so, [-7,∞)

-first label the equation with a,b,and c. s=-16t²+128t +0 a b c -next, to find the max value, solve for h and k. h=-b/2a h=-128/2(-16) h=-128/-32 h=4 k=f(h)=-16(4)²+128(4) k=-256+512 k=256 Therefore, the max height the ball can reach is 256ft.