# Sample quiz on stretches and compressions of functions Main home here.

1. Let $f(x)$ be a function. For $a> 1$, the transformation $af(x)$ amounts to $\cdots$?
A: a vertical stretch by a factor of $a$
B: a vertical stretch by a factor of $\frac{1}{a}$
C: a horizontal stretch by a factor of $a$
D: a horizontal stretch by a factor of $\frac{1}{a}$
2. Let $f(x)$ be a function. For $0< a < 1$, the transformation $af(x)$ amounts to $\cdots$?
A: a vertical stretch by a factor of $a$
B: a horizontal stretch by a factor of $\frac{1}{a}$
C: a horizontal stretch by a factor of $a$
D: a vertical compression by a factor of $a$
3. Let $f(x)$ be a function. For $0< k < 1$, the transformation $f(kx)$ amounts to $\cdots$?
A: a horizontal stretch by a factor of $k$
B: a horizontal stretch by a factor of $\frac{1}{k}$
C: a vertical stretch by a factor of $k$
D: a vertical compression by a factor of $\frac{1}{k}$
4. Let $f(x)$ be a function. For $k > 1$, the transformation $f(kx)$ amounts to $\cdots$?
A: a horizontal compression by a factor of $k$
B: a vertical stretch by a factor of $k$
C: a horizontal compression by a factor of $\frac{1}{k}$
D: a vertical compression by a factor of $\frac{1}{k}$
5. Let $f(x)=x^2$. Find the image of the point $(2,4)$ after the transformation $g(x)=5f(x)$.
A: $(10,20)$
B: $(4,16)$
C: $(2,20)$
D: $(2,25)$
6. Let $f(x)=\sqrt{x}$. Find the image of the point $(4,2)$ under the transformation $g(x)=f(2x)$.
A: $(2,2)$
B: $(8,2)$
C: $(2,1)$
D: $(16,8)$
7. Let $f(x)=\sqrt{x}$. Relative to $f(x)$, what transformation produces $g(x)=2\sqrt{x}$?
A: a vertical compression by a factor of $\frac{1}{2}$
B: a horizontal stetch by a factor of $2$
C: a vertical stretch by a factor of $\sqrt{2}$
D: a vertical stretch by a factor of $2$.
8. Let $f(x)=\sqrt{x}$. Relative to $f(x)$, what transformation produces $g(x)=\sqrt{2x}$?
A: a horizontal compression by a factor of $\frac{1}{2}$
B: a horizontal compression by a factor of $2$
C: a horizontal stretch by a factor of $\sqrt{2}$
D: a horizontal compression by a factor of $\frac{1}{\sqrt{2}}$
9. Given $f(x)=\sqrt{x}$, one can obtain $g(x)=\sqrt{9x}$ via a horizontal compression (factor $k$) and separately via a vertical stretch (factor $a$). Find $k$ and $a$.
A: $k=\frac{1}{9},~a=\frac{1}{9}$
B: $k=9,~a=9$
C: $k=\frac{1}{9},~a=3$
D: $k=3,~a=3$
10. Let $f(x)=x^2$. Find a horizontal compression that will have the same effect as the vertical stretch $g(x)=4x^2$.
A: a horizontal compression by a factor of $\frac{1}{4}$
B: a horizontal compression by a factor of $\frac{1}{2}$
C: a horizontal compression by a factor of $\frac{1}{8}$
D: a horizontal compression by a factor of $\frac{1}{16}$
11. Describe the transformation needed to produce $g(x)=\frac{4}{x}$ from $f(x)=\frac{1}{x}$.
A: a vertical compression by a factor of $\frac{1}{4}$
B: a horizontal stetch by a factor of $2$
C: a horizontal compression by a factor of $\frac{1}{2}$
D: a vertical stretch by a factor of $4$
12. Describe the transformation needed to produce $g(x)=|5x|$ from $f(x)=|x|$.
A: a horizontal compression by a factor of $\frac{1}{5}$
B: a vertical compression by a factor of $\frac{1}{5}$
C: a horizontal translation of $5$ units to the right
D: a vertical translation of $5$ units up
13. What function results from stretching $f(x)=x^2$ vertically by a factor of $8$?
A: $g(x)=x^2+8$
B: $g(x)=\frac{1}{8}x^2$
C: $g(x)=(8x)^2$
D: $g(x)=8x^2$
14. What function results from compressing $f(x)=|x|$ horizontally by a factor of $\frac{2}{3}$?
A: $g(x)=|\frac{3}{2}x|$
B: $g(x)=|\frac{2}{3}x|$
C: $g(x)=|x-\frac{2}{3}|$
D: $g(x)=|x+\frac{3}{2}|$
15. Let $f(x)=\sqrt{x}$. What is the domain of the new function $g(x)=\sqrt{10x}$?
A: $\{x\in\mathbb{R}~:~x\geq 10\}$
B: $\{x\in\mathbb{R}~:~x\leq 10\}$
C: $\{x\in\mathbb{R}~:~x\geq 0\}$
D: $\{x\in\mathbb{R}~:~x\geq \frac{1}{10}\}$
16. Let $f(x)=\frac{1}{x}$. What is the domain of the transformed function $g(x)=\frac{1}{3x}$?
A: $\{x\in\mathbb{R}~:~x\geq 3\}$
B: $\{x\in\mathbb{R}~:~x\neq 3\}$
C: $\{x\in\mathbb{R}~:~x\neq 0\}$
D: $\{x\in\mathbb{R}~:~x\neq \frac{1}{3}\}$
17. Let $f(x)=x^2$. After being horizontally compressed by $\frac{1}{2}$, then vertically stretched by a factor of $2$, the resulting function is $\cdots$?
A: $g(x)=x^2$
B: $g(x)=8x^2$
C: $g(x)=4x^2$
D: $g(x)=\frac{1}{4}x^2$
18. Let $f(x)=\sqrt{x}$. Find the range of the transformed function $g(x)=\sqrt{4x}$.
A: $\{y\in\mathbb{R}~:~y\geq 0\}$
B: $\{y\in\mathbb{R}~:~y\geq 4\}$
C: $\{y\in\mathbb{R}~:~y\geq 2\}$
D: $\{y\in\mathbb{R}~:~y\leq 0\}$
19. Let $f(x)=|x|$. Find the image of the point $(-1,1)$ after the transformation $g(x)=2f(x)$.
A: $(-1,1)$
B: $(-2,1)$
C: $(-2,2)$
D: $(-1,2)$
20. Let $f(x)=\frac{1}{x}$. Find the image of the point $\left(\frac{1}{2},2\right)$ after the transformation $g(x)=f(\frac{1}{2}x)$.
A: $\left(\frac{1}{4},2\right)$
B: $\left(\frac{1}{2},\frac{1}{2}\right)$
C: $\left(1,\frac{1}{2}\right)$
D: $(1,2)$