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Function notation and evaluating functions — ACT practice questions

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• 45 questions on the paper
• 63 practice questions in the app
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Practice 63 Function notation and evaluating functions questions in the app

What this topic is

Function notation and evaluating functions on the ACT Mathematics test covers reading f(x) style notation, substituting a given input into a formula, and interpreting a recorded function value in context.

Sample questions

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

Question 1Easier

A model rocket is launched vertically. Its height $h(t)$ meters after $t$ seconds is modeled by $h(t)=-5t^2+40t+12$. What is the height, in meters, of the rocket 4 seconds after launch?

A72✗ Not this oneB92✓ CorrectC112✗ Not this oneD132✗ Not this one

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Answer: B — 92

$h(4)=-5(16)+40(4)+12=-80+160+12=92$.

Question 2Easier

A battery laboratory uses $p(n)$ for the performance index of a battery after charging cycle $n$. A technician records $p(6)=53$. Which of the following correctly interprets this record?

AAfter charging cycle 6, the performance index is 53.✓ CorrectBAfter charging cycle 53, the performance index is 6.✗ Not this oneCThe performance index increases by 53 during each of 6 cycles.✗ Not this oneDThe sum of the performance indices through cycle 6 is 53.✗ Not this one

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Answer: A — After charging cycle 6, the performance index is 53.

In p(6) = 53, the input 6 is the charging-cycle number and the output 53 is the corresponding performance index.

Question 3Easier

Let $q(x)=x^2-4$ and $r(x)=2x+1$. What is $q(r(3))$?

A21✗ Not this oneB25✗ Not this oneC45✓ CorrectD49✗ Not this one

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Answer: C — 45

First, $r(3)=2(3)+1=7$. Then $q(r(3))=q(7)=7^2-4=45$.

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