Key features and transformations of graphs — ACT practice questions

Key features and transformations of graphs on the ACT Mathematics test cover intercepts, slope, domain, and how a graph stretches or shifts when a function is rewritten. Students must find an intercept from slope-intercept form, recover a stretch factor from matching outputs, and rewrite a domain after a horizontal translation. Questions are multiple choice and often describe the graph in words or algebra instead of showing it, so common traps are swapping x- and y-intercepts, treating a vertical stretch as a horizontal one, or shifting the domain the wrong way. Answer choices tend to be similar numbers or inequalities that differ by a sign.

Section: Mathematics 45 questions on the paper
53 practice questions in the app

Sample questions

Question 1

The domain of $f$ is all real $x$ such that $x\geq-2$ . Let $g(x)=f(x+6)$ . Which of the following inequalities describes the domain of $g$ ?

A $x\geq 4$
B $x\leq -8$
C $x\leq 4$
D $x\geq -8$

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Answer: D — $x\geq -8$

The input to $f$ must satisfy $x+6\geq -2$ . Subtracting 6 gives $x\geq -8$ , which is the domain of $g$ .

Question 2

The graph of $y=g(x)$ is a vertical stretch of the graph of $y=f(x)$ , where $g(x)=af(x)$ and $a>0$ . If $f(4)=6$ and $g(4)=15$ , what is the value of $a$ ?

A0.4
B2.5
C9
D21

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Answer: B — 2.5

Since $g(4)=a f(4)$ , the given values yield $15=6a$ . Thus, $a=2.5$ .

Question 3

In the standard $(x,y)$ coordinate plane, a line has slope -2 and $y$ -intercept 6. What is the $x$ -intercept of this line?

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Answer: C — 3

The equation is $y=-2x+6$ . Setting $y=0$ gives $x=3$ . The number 6 is the $y$ -intercept.

Practice 53 Key features and transformations of graphs questions in the app

Key features and transformations of graphs — ACT practice questions

Sample questions

More ACT topics

Mathematics