Precalculus Functions, Domain and Range Test Solutions and Scoring (PDF)
This precalculus functions test answers for Precalculus covers functions, domain and range (Common Core F-IF.A.1, F-IF.A.2, F-IF.B.5), with a free PDF to print.
Precalculus · Common Core State Standards: F-IF.A.1, F-IF.A.2, F-IF.B.5
Precalculus functions test answers: worked solutions
Question 1 – Evaluate [2 pts]
\(f(-1)=1+3+2=6\). \(f(4)=16-12+2=6\).
\(f(-1)=6,\ f(4)=6\)
Scoring: 1 point for each correct value.
Question 2 – Function or not [2 pts]
Each input appears once. Repeated outputs are allowed.
Yes, it is a function
Scoring: 1 point for the correct answer, 1 point for the reason (each input has one output).
Question 3 – Domain with root and fraction [2 pts]
\(x+2\ge 0\) gives \(x\ge -2\). The denominator excludes \(x=5\).
\([-2,5)\cup(5,\infty)\)
Scoring: 1 point for the root condition \(x\ge -2\), 1 point for excluding 5 and correct notation.
Question 4 – Domain of a rational function [2 pts]
\(x^{2}-9=0\) gives \(x=\pm 3\).
\((-\infty,-3)\cup(-3,3)\cup(3,\infty)\)
Scoring: 1 point for finding both excluded values, 1 point for notation.
Question 5 – Read a graph [3 pts]
(a) Domain \([-3,3]\); range \([-2,2.5]\). (b) \(f(0)=-2\). (c) \(\frac12x^{2}-2=0\) gives \(x=\pm 2\).
Domain \([-3,3]\); range \([-2,2.5]\); \(f(0)=-2\); \(x=\pm 2\)
Scoring: 1 point for domain and range together, 1 point for f(0), 1 point for both zeros.
Question 6 – Piecewise function [2 pts]
\(f(-3)=2(-3)+1=-5\). \(f(0)=1\) because \(0\le 0\). \(f(3)=9-4=5\).
\(-5,\ 1,\ 5\)
Scoring: 1 point for f(-3) and f(3) together, 1 point for f(0) using the correct piece.
Question 7 – Difference quotient [2 pts]
\(f(x+h)-f(x)=2xh+h^{2}-h\). Divide by \(h\).
\(2x+h-1\)
Scoring: 1 point for expanding f(x+h) correctly, 1 point for simplifying.
Question 8 – Projectile model [3 pts]
(a) \(h(0)=4\) ft. (b) The vertex is at \(t=\frac{-48}{2(-16)}=1.5\), and \(h(1.5)=-36+72+4=40\) ft. (c) From launch until landing: \(0\le t\le 3.08\) (the positive root of \(h(t)=0\)).
\(4\) ft; \(40\) ft; \([0,\ 3.08]\)
Scoring: 1 point for each part.
Question 9 – Rental cost model [2 pts]
\(R(250)=30+100=130\). Solve \(30+0.40d=98\): \(0.40d=68\), \(d=170\).
\(\$130\); \(170\) miles
Scoring: 1 point for R(250), 1 point for solving for d.
Total score
20 points
Key facts behind this precalculus functions test answers
- A relation is a function only if each input has exactly one output (vertical line test).
- Domain: allowed inputs. Range: outputs that actually occur.
- Exclude values that make a denominator 0 or an even-root radicand negative.
- Interval notation uses brackets for included endpoints and parentheses for excluded ones.
- A piecewise function uses a different rule on each part of its domain.
How to use this precalculus functions test answers
Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.
All Precalculus chapters: Precalculus math.
