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Key features and transformations of graphs — ACT practice questions

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• 45 questions on the paper
• 53 practice questions in the app
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Practice 53 Key features and transformations of graphs questions in the app

What this topic is

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.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

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$x\geq 4$✗ Not this oneB$x\leq -8$✗ Not this oneC$x\leq 4$✗ Not this oneD$x\geq -8$✓ Correct

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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 2Easier

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✗ Not this oneB2.5✓ CorrectC9✗ Not this oneD21✗ Not this one

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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 3Easier

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

A6✗ Not this oneB$-2$✗ Not this oneC3✓ CorrectD$-3$✗ Not this one

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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.

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