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Function notation and evaluating functions — ACT practice questions

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. A student must evaluate a quadratic or linear rule at a stated time, explain what an output after a charging cycle means, and compute a composition from the inside out. Items are multiple-choice: numeric heights or outputs, verbal readings of a recorded value, or a single composed result. Typical traps are reversing composition order, treating the notation as multiplication, swapping input with output, and sign mistakes in substitution.

  • Section: Mathematics 45 questions on the paper
  • 60 practice questions in the app

Sample questions

Question 1

A model rocket is launched vertically. Its height h(t)h(t) meters after tt seconds is modeled by h(t)=−5t2+40t+12h(t)=-5t^2+40t+12. What is the height, in meters, of the rocket 4 seconds after launch?

  1. A72
  2. B92
  3. C112
  4. D132
Show answer

Answer: B — 92

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

Question 2

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

  1. AAfter charging cycle 6, the performance index is 53.
  2. BAfter charging cycle 53, the performance index is 6.
  3. CThe performance index increases by 53 during each of 6 cycles.
  4. DThe sum of the performance indices through cycle 6 is 53.
Show answer

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 3

Let q(x)=x2−4q(x)=x^2-4 and r(x)=2x+1r(x)=2x+1. What is q(r(3))q(r(3))?

  1. A21
  2. B25
  3. C45
  4. D49
Show answer

Answer: C — 45

First, r(3)=2(3)+1=7r(3)=2(3)+1=7. Then q(r(3))=q(7)=72−4=45q(r(3))=q(7)=7^2-4=45.

Practice 60 Function notation and evaluating functions questions in the app

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