Precalculus Functions, Domain and Range Worksheet (PDF)

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

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This precalculus functions worksheet 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.

These 20 problems practice functions, domain and range (Common Core F-IF.A.1, F-IF.A.2 and F-IF.B.5). Start with evaluating and finding domains, then read graphs, use piecewise rules and difference quotients.

Precalculus · Common Core State Standards: F-IF.A.1, F-IF.A.2, F-IF.B.5

Precalculus functions worksheet: exercises 1 to 10

Exercise 1 – Evaluate a quadratic

Evaluate $f(3)$ for $f(x)=2x^{2}-5x+1$.

Exercise 2 – Evaluate a cubic

Evaluate $g(-2)$ for $g(x)=x^{3}-4x$.

Exercise 3 – Is it a function?

Input-output table.

Decide whether the table represents $y$ as a function of $x$. Explain.

Exercise 4 – Domain of a line

Find the domain of $f(x)=3x-7$. Write it in interval notation.

Exercise 5 – Domain with a denominator

Find the domain of $h(x)=\frac{1}{x-4}$.

Exercise 6 – Domain with a root

Find the domain of $f(x)=\sqrt{2x+6}$.

Exercise 7 – Root and denominator together

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

Exercise 8 – Range of a shifted parabola

Find the range of $f(x)=x^{2}+3$.

Exercise 9 – Read a graph

Graph of f on a closed interval.

Use the graph to find the domain, the range, and $f(2)$.

Exercise 10 – Piecewise values

Let $f(x)=x+4$ when $x< 1$ and $f(x)=x^{2}$ when $x\ge 1$. Find $f(-2)$, $f(1)$ and $f(3)$.

Exercises 11 and up

Exercise 11 – Vertical line test

A circle and a vertical line.

Does the circle $x^{2}+y^{2}=9$ represent $y$ as a function of $x$? Explain.

Exercise 12 – Domain of a model

A fence uses 40 ft of wire to enclose a rectangle of width $w$ feet. Its area is $A(w)=w(20-w)$. Find the realistic domain of $A$.

Exercise 13 – Reciprocal of a root

Find the domain of $f(x)=\frac{1}{\sqrt{x-3}}$.

Exercise 14 – Solve f(x) = value

For $f(x)=4x-1$, find $x$ when $f(x)=11$.

Exercise 15 – Input for a quadratic output

For $f(x)=x^{2}-2x$, find every $x$ with $f(x)=8$.

Exercise 16 – Difference quotient

For $f(x)=x^{2}+1$, simplify $\frac{f(2+h)-f(2)}{h}$ for $h\neq 0$.

Exercise 17 – Taxi fare

A taxi in Austin charges $C(m)=4+2.5m$ dollars for a ride of $m$ miles. Find the fare for a $6.4$-mile ride, and find how far Priya can ride for $\$34$.

Exercise 18 – Height of a ball

Height of Diego’s ball.

Diego throws a ball so its height in feet after $t$ seconds is $h(t)=-16t^{2}+64t+5$. Find $h(0)$, $h(1)$ and $h(2)$, then state the range of heights while the ball is in the air (the ball lands at about $t\approx 4.08$ s).

Exercise 19 – Data plan

A data plan with a flat fee.

Sofia’s plan costs $\$25$ for up to $5$ GB, plus $\$8$ for each GB over $5$. Find the cost for $3$ GB, $5$ GB and $9.5$ GB, and state the range of the cost function.

Exercise 20 – Semicircle function

Graph of f.

Find the domain and range of $f(x)=\sqrt{9-x^{2}}$.

Key facts behind this precalculus functions worksheet

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 worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the precalculus functions worksheet as a PDF with the button below and keep it with your notes.

All Precalculus chapters: Precalculus math.

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