ACT · Elementary Algebra · Substitution and evaluation
Question act-q-00313
Medium Multiple choice No calculator
The question
If f(x) = 3x² − 1, what is the value of f(6)?
- -107
- 107
- 17
- 108
Show answer & worked solution
Answer: 107
Worked solution. Substitute x = 6: f(6) = 3 × (6)² − 1 = 3 × 36 − 1 = 108 − 1 = 107.
Why each wrong choice is wrong. Forgetting to square the input is the dominant error — the linear-substitution distractor catches it.
Test-day tactic. Substitute with parentheses around the input. (6)² always equals 36, regardless of the sign of 6.
About this question type
A value or set of values is given for the variables; substitute and compute. The arithmetic can be tricky when negatives or fractions are involved.
You will see a question shaped like this one on roughly every other official ACT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.