Question 1

The black curve is the graph of $y=f(x)$. What equation made the red curve?

Accepted Answer

$y=f(x+5)$

Answer

$y=f(x)-5$

Answer

$y=f(x-5)$

Answer

$y=f(x)+5$

Question 2

The black curve is the graph of $y=f(x)$. What equation made the red curve?

Accepted Answer

$y=f(x-5)$

Answer

$y=f(x)+5$

Answer

$y=f(x)-5$

Answer

$y=f(x+5)$

Question 3

The black curve is the graph of $y=f(x)$. What equation made the red curve?

Accepted Answer

$y=f(2x)$

Answer

$y=2f(x)$

Answer

$y=\frac{f(x)}{2}$

Answer

$y=f(\frac{x}{2})$

Question 4

The black curve is the graph of $y=f(x)$. What equation made the red curve?

Accepted Answer

$y=f(\frac{x}{2})$

Answer

$y=2f(x)$

Answer

$y=\frac{f(x)}{2}$

Answer

$y=f(2x)$

Question 5

The graph of $y=f(x)$ is reflected in the $y-$axis and stretched twice as far from the $x-$axis.

Accepted Answer

$y=2f(-x)$

Answer

$y=\frac{1}{2}f(-x)$

Answer

$y=-f(\frac{1}{2}x)$

Answer

$y=-f(2x)$

Question 6

The graph of $y=f(x)$ is reflected in the $x-$axis and stretched twice as far from the $y-$axis.

Accepted Answer

$y=-f(\frac{1}{2}x)$

Answer

$y=\frac{1}{2}f(-x)$

Answer

$y=-f(2x)$

Answer

$y=2f(-x)$

Question 7

The graph of $y=f(x)$ is transformed by vertical dilation factor of $5$, followed by translation by $\left( \begin{array}{c} 6 \ 0 \end{array} ight)$ (meaning  a horizontal translation of $6$ and vertical translation of $0$).

Accepted Answer

$y=5f(x-6)$

Answer

$y=5f(x)+6$

Answer

$y=5f(x)-6$

Answer

$y=5f(x+6)$

Question 8

The graph of $y=f(x)$ is transformed by horizontal dilation factor of $5$, followed by translation by $\left( \begin{array}{c} 0 \ -2 \end{array} ight)$ (meaning  a horizontal translation of $0$ and vertical translation of $-2$).

Accepted Answer

$y=f(\frac x{5})-2$

Answer

$y=f(5x)-2$

Answer

$y=f(\frac {x+2}{5})$

Answer

$y=5f(x)-2$

Question 9

The graph of $y=f(x)$ is transformed by vertical dilation factor of $\frac 3{4}$, followed by translation by $\left( \begin{array}{c} -1 \ 2 \end{array} ight)$ (meaning  a horizontal translation of $-1$ and vertical translation of $2$).

Accepted Answer

$y=\frac 3{4}f(x+1)+2$

Answer

$y=\frac 3{4}f(x-1)+2$

Answer

$y=\frac 3{4}f(x-2)-1$

Answer

$y=f(\frac 3{4}x-1)+2$

Question 10

The graph of $y=f(x)$ is transformed by horizontal dilation factor of $1/4$, followed by translation by $\left( \begin{array}{c} 0 \ 1 \end{array} ight)$ (meaning  a horizontal translation of $0$ and vertical translation of $1$).

Accepted Answer

$y=f(4x)+1$

Answer

$y=4f(x-1)$

Answer

$y=f(x+4)+1$

Answer

$y=f(\frac x{4})+1$

Question 11

The graph of $y=f(x)$ is transformed by horizontal dilation factor of $3$, followed by translation by $\left( \begin{array}{c} 1 \ 0 \end{array} ight)$ (meaning  a horizontal translation of $1$ and vertical translation of $0$).

Accepted Answer

$y=f(\frac {x-1}{3})$

Answer

$y=f(\frac {x}{3}-1)$

Answer

$y=f(3(x-1))$

Answer

$y=f(3x-1)$

Question 12

The graph of $y=f(x)$ is transformed by horizontal dilation factor of $\frac2{3}$, followed by translation by $\left( \begin{array}{c} -1 \ 0 \end{array} ight)$ (meaning  a horizontal translation of $-1$ and vertical translation of $0$).

Accepted Answer

$y=f(\frac {3(x+1)}{2})$

Answer

$y=f(\frac {2x}{3}+1)$

Answer

$y=f(\frac {2(x+1)}{3})$

Answer

$y=f(\frac {3}{2}x+1)$

Question 13

The function $f(x)=\frac1{x}$ is transformed to $g(x)=\frac2{x+3}-1$ by a vertical dilation factor $q$ followed by translation by $\left( \begin{array}{c} r \ m \end{array} ight)$. Find the values of $q, r$ and $m$.

Accepted Answer

$q=2, r=-3, m=-1$

Answer

$q=2, r=-3, m=1$

Answer

$q=2, r=3, m=-1$

Answer

$q=\frac1{2}, r=3, m=-1$

Question 14

The function $f(x)=(x-1)^2$ is transformed to $g(x)=-2(x-1)^2 +3$ by a vertical dilation factor $q$ followed by translation by $\left( \begin{array}{c} r \ m \end{array} ight)$. Find the values of $q, r$ and $m$.

Accepted Answer

$q=-2, r=0, m=3$

Answer

$q=-\frac1{2}, r=1, m=3$

Answer

$q=-2, r=-1, m=3$

Answer

$q=-2, r=1, m=3$

Question 15

The function $f(x)=2e^x$ is transformed to $g(x)=e^{x-1}$ by a vertical dilation factor $q$ followed by translation by $\left( \begin{array}{c} r \ m \end{array} ight)$. Find the values of $q, r$ and $m$.

Accepted Answer

$q=\frac1{2}, r=1, m=0$

Answer

$q=2, r=-1, m=0$

Answer

$q=\frac1{2}, r=0, m=-1$

Answer

$q=1, r=\frac1{2}, m=0$

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