Functions & Graphs Quiz (Domain, Range, Transformations)

Question 1

Find the domain of $f(x)=\sqrt{x-3}$.

Accepted Answer

$[3,\infty)$

Answer

$(-\infty,\infty)$

Answer

$(-\infty,3]$

Answer

$(3,\infty)$

Question 2

A graph of $y=f(x)$ is shifted right 3 units and down 2 units. Which equation represents the new graph?

Accepted Answer

$y=f(x-3)-2$

Answer

$y=f(x-3)+2$

Answer

$y=f(x+3)-2$

Answer

$y=f(x)-3-2$

Question 3

Let $f(x)=\sqrt{x+1}$ and $g(x)=\dfrac{1}{x}$. What is the domain of $(f\circ g)(x)=f(g(x))$?

Accepted Answer

$(-\infty,0)\cup[1,\infty)$

Answer

$x>0$

Answer

$(-\infty,-1]\cup(0,\infty)$

Answer

$(-\infty,-1)\cup(1,\infty)$

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