Radical and rational functions — ACT practice questions

Question 1

Which of the following describes the real-number domain of the function $h(x)=\dfrac{(x-2)^{1/2}}{x-6}$?

1. A$x\ge 2$
2. B$x\ge 2$ and $x\ne 6$
3. C$x>2$ and $x\ne 6$
4. DAll real $x$ except 6

Question 2

Given that $f(x)=\sqrt[3]{4x+5}$, which statement correctly describes the domain and range of $f$?

1. AThe domain is $\left[-\dfrac{5}{4},\infty\right)$, and the range is all real numbers.
2. BThe domain is all real numbers, and the range is all real numbers.
3. CThe domain is all real numbers, and the range is $[0,\infty)$.
4. DThe domain excludes $-\dfrac{5}{4}$, and the range excludes 0.

Question 3

Which of the following statements best describes the graph of $y=\dfrac{(x-2)(x+5)}{(x-2)(x+1)}$ at $x=2$?

1. AThere is a hole at $x=2$.
2. BThere is a vertical asymptote at $x=2$.
3. CThe graph crosses the $x$-axis at $x=2$.
4. DThe graph has a horizontal asymptote $y=2$.