Practice Piecewise Function in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A piecewise function is defined by different formulas on different non-overlapping intervals of its domain, with the applicable formula determined by the input value.

A piecewise function is like a rulebook: look up which rule applies to your input value, then use only that rule to compute the output.

Showing a random 20 of 50 problems.

Example 1

hard
For f(x)={2x+1x<0x2−3x≥0, find the range on [−2,2].

Example 2

hard
The greatest integer (floor) function is ⌊x⌋. Express ⌊x⌋ on [0,3) as a piecewise function.

Example 3

medium
For f(x)={2xx<1x+1x≥1, is f continuous at x=1?

Example 4

medium
For f(x)={−xx<0x2x≥0, find the range on [−3,2].

Example 5

easy
Should the intervals of a piecewise function overlap?

Example 6

easy
In the absolute value ∣x∣={xx≥0−xx<0, find ∣−5∣.

Example 7

challenge
For f(x)={x2x<12x−1x≥1, find all x with f(x)=1.

Example 8

easy
For f(x)={xx<0x+1x≥0, find f(−2).

Example 9

medium
Find the value of a that makes f(x)={ax+1x≤2x2−1x>2 continuous at x=2.

Example 10

easy
For the same f, find f(3).

Example 11

easy
Evaluate f(x)={x2x<02x+1x≥0 at x=−3, x=0, and x=4.

Example 12

easy
For the same f, find f(4).

Example 13

easy
Write the absolute value ∣x∣ as a piecewise function.

Example 14

easy
How many pieces does sgn(x)={1x>00x=0−1x<0 have?

Example 15

medium
Determine whether f(x)={x+1x<23x=22x−1x>2 is continuous at x=2.

Example 16

medium
Solve f(x)=4 for f(x)={2x+6x<0x2x≥0.

Example 17

medium
For f(x)={−xx<0x20≤x≤24x>2, find f(0) and f(2).

Example 18

hard
Find the value of c so that f(x)={cx+1x≤3x2−2x>3 is continuous at x=3.

Example 19

medium
Does f(x)={1x≤0x+1x>0 have a jump at x=0?

Example 20

easy
For f(x)={5x≤12xx>1, find f(1).
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