begin{table}[]
defarraystretch{1.5}%
begin{tabular}{|l|l|}
hline
Transformation & Description \ hline
$y=f(x)+c$ & begin{tabular}[c]{@{}l@{}}vertical translation of\ $c$ units upwardend{tabular} \ hline
$y=f(x+d)$ & begin{tabular}[c]{@{}l@{}}horizontal translation of $d$ units\ to the leftend{tabular} \ hline
$y=acdot f(x)$ & begin{tabular}[c]{@{}l@{}}vertical stretching, multiplies\ the amplitude by $a$end{tabular} \ hline
$y=f(kx)$ & begin{tabular}[c]{@{}l@{}}horizontal compression, divides\ the period by $k$end{tabular} \ hline
$y=-f(x)$ & begin{tabular}[c]{@{}l@{}}reflecting the function in\ the $x$-axisend{tabular} \ hline
$y=f(-x)$ & begin{tabular}[c]{@{}l@{}}reflecting the function in \ the $y$-axisend{tabular} \ hline
end{tabular}
end{table}

begin{table}[]
defarraystretch{1.5}%
begin{tabular}{|l|l|}
hline
Transformation & Description \ hline
a) $y=3cos x$ & begin{tabular}[c]{@{}l@{}}vertical stretching\ multiplies the amplitude by 3end{tabular} \ hline
b) $y=sin(x-50^circ)$ & begin{tabular}[c]{@{}l@{}}horizontal translation\ shifts $50^circ$ to the rightend{tabular} \ hline
c) $y=-cos x$ & reflection over $x$-axis \ hline
d) $y=sin(5x)$ & begin{tabular}[c]{@{}l@{}}horizontal compression\ divides the period by 5end{tabular} \ hline
e) $y=cos x -6$ & begin{tabular}[c]{@{}l@{}}vertical translation\ shifts $-6$ downend{tabular} \ hline
f) $y=cos(x+20^circ)$ & begin{tabular}[c]{@{}l@{}}horizontal translation\ shifts $20^circ$ to the leftend{tabular} \ hline
end{tabular}
end{table}

begin{table}[]
defarraystretch{1.5}%
begin{tabular}{|l|l|}
hline
Transformation & Description \ hline
$y=f(x)+c$ & begin{tabular}[c]{@{}l@{}}vertical translation of\ $c$ units upwardend{tabular} \ hline
$y=f(x+d)$ & begin{tabular}[c]{@{}l@{}}horizontal translation of $d$ units\ to the leftend{tabular} \ hline
$y=acdot f(x)$ & begin{tabular}[c]{@{}l@{}}vertical stretching, multiplies\ the amplitude by $a$end{tabular} \ hline
$y=f(kx)$ & begin{tabular}[c]{@{}l@{}}horizontal compression, divides\ the period by $k$end{tabular} \ hline
$y=-f(x)$ & begin{tabular}[c]{@{}l@{}}reflecting the function in\ the $x$-axisend{tabular} \ hline
$y=f(-x)$ & begin{tabular}[c]{@{}l@{}}reflecting the function in \ the $y$-axisend{tabular} \ hline
end{tabular}
end{table}

begin{table}[]
defarraystretch{1.5}%
begin{tabular}{|l|l|}
hline
Transformation & Description \ hline
a) $y=sin x +2$ & the axis is shifted upwards by 2 \ hline
b) $y=4sin x$ & amplitude is multiplied by 4 \ hline
c) $y=cos (8x)$ & period is divided by 8 \ hline
begin{tabular}[c]{@{}l@{}}d) $y=sin(2x+30)$\ $implies y=sin(2(x+15))$end{tabular} & begin{tabular}[c]{@{}l@{}}period is divided by 2 and\ horizontally translated \ to the left by 15end{tabular} \ hline
e) $y=0.25cos x$ & amplitude is divided by 4 \ hline
f) $y=sin(0.5x)$ & period is multiplied by 2 \ hline
end{tabular}
end{table}

All stretches/compression will affect the period and amplitude, thus we eliminate options b and d. Vertical translation changes the equation of the axis so we can eliminate c. The two that remains are options a) reflection in $x$-axis and e) horizontal translation.