Precalculus Functions, Domain and Range Test with Point Values (PDF)

Precalculus math test: Functions, Domain and Range – Maths PDF

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This precalculus functions test 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.

This 20-point test covers function notation, domain and range, graphs, piecewise functions and a projectile model (F-IF.A.1, F-IF.A.2, F-IF.B.5). You have 45 minutes. Show your work.

Time and points

About this test

Grade: Precalculus
Chapter: Functions, Domain and Range
Standards: F-IF.A.1, F-IF.A.2, F-IF.B.5
Time: 45 minutes
Total: 20 points

Precalculus functions test: questions

Question 1 – Evaluate [2 pts]

Let $f(x)=x^{2}-3x+2$. Find $f(-1)$ and $f(4)$.

Question 2 – Function or not [2 pts]

Table of values.

Is $y$ a function of $x$? Explain.

Question 3 – Domain with root and fraction [2 pts]

Find the domain of $f(x)=\frac{\sqrt{x+2}}{x-5}$ in interval notation.

Question 4 – Domain of a rational function [2 pts]

Find the domain of $g(x)=\frac{1}{x^{2}-9}$ in interval notation.

Question 5 – Read a graph [3 pts]

Graph of f on a closed interval.

Use the graph. (a) State the domain and range.

(b) Find $f(0)$.

Question 6 – Piecewise function [2 pts]

Let $f(x)=2x+1$ for $x\le 0$ and $f(x)=x^{2}-4$ for $x>0$. Find $f(-3)$, $f(0)$ and $f(3)$.

Question 7 – Difference quotient [2 pts]

Simplify $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}-x$, where $h\neq 0$.

Question 8 – Projectile model [3 pts]

Ball thrown by Ethan.

Ethan tosses a ball. Its height in feet after $t$ seconds is $h(t)=-16t^{2}+48t+4$.

(a) Find the starting height.

(b) Find the maximum height.

Question 9 – Rental cost model [2 pts]

A truck rental costs $R(d)=30+0.40d$ dollars for $d$ miles. Find $R(250)$, and find the miles driven when the cost is $\$98$.

Key facts behind this precalculus functions test

Key facts

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

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Precalculus chapters: Precalculus math.

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