# Sample quiz on translations of functions Main home here.

1. If $f(x)$ is a function, the transformation $f(x-3)$ amounts to $\cdots$?
a horizontal translation of $3$ units to the left
a horizontal compression by a factor of $3$
a horizontal translation of $3$ units to the right
a horizontal translation of $f(3)$ units to the right
2. If $f(x)$ is a function, the transformation $f(x)+3$ amounts to $\cdots$?
a vertical translation of $3$ units up
a vertical translation of $3$ units down
a horizontal translation of $3$ units to the right
a horizontal translation of $3$ units to the left.
3. Let $f(x)=\sqrt{x}$ be the parent square root function. What is the correct expression for $f(x-2)$?
$\sqrt{2-x}$
$\sqrt{x}-2$
$\sqrt{x+2}$
$\sqrt{x-2}$
4. Let $f(x)=\frac{1}{x}$. Relative to $f(x)$, the function $g(x)=\frac{1}{x+2}$ can be obtained by $\cdots$?
a horizontal translation of $2$ units to the left
a horizontal translation of $2$ units to the right
a vertical translation of $2$ units up
a vertical translation of $2$ units down.
5. If $f(x)=x^2$ is translated horizontally $3$ units to the left, what is the resulting function?
$(x-3)^2$
$x^2-3$
$(x+3)^2$
$x^2+3$
6. Given that $f(x)=|x-1|$, find a transformation needed to obtain $g(x)=|x|$.
a horizontal translation of $1$ unit to the left
a horizontal translation of $1$ unit to the right
a vertical translation of $1$ unit up
a vertical translation of $1$ unit down.
7. Given that $f(x)=\sqrt{x}$, find the domain of the transformed function $f(x+4)$.
$\{x\in\mathbb{R}~|~x\leq -4\}$
$\{y\in\mathbb{R}~|~y\geq -4\}$
$\{x\in\mathbb{R}~|~x\geq -4\}$
$\{y\in\mathbb{R}~|~y\leq -4\}$
8. Find the function resulting from a vertical translation of $\frac{1}{x}$ by $3$ units up.
$\frac{1-3x}{x}$
$\frac{3x}{1+3x}$
$\frac{1}{x+3}$
$\frac{1+3x}{x}$
9. Find the domain of $f(x)=\frac{1}{x}$ after it undergoes a horizontal translation of $5$ units to the left
$\{x\in\mathbb{R}~:x\neq 5\}$
$\{x\in\mathbb{R}~:x\geq -5\}$
$\{x\in\mathbb{R}~:x\leq -5\}$
$\{x\in\mathbb{R}~:x\neq -5\}$
10. What transformation(s) is(are) needed to convertex $f(x)=x^2$ to $g(x)=x^2+4x+4$?
a horizontal translation of $4$ units to the left, followed by a vertical translation of $4$ units up
a horizontal translation of $4$ units to the right, followed by a vertical translation of $4$ untis up
a horizontal translation of $2$ units to the left
a horizontal translation of $2$ units to the right