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1.04 Piecewise functions

Adaptive
Worksheet

Interactive practice questions

Consider the piecewise function given below:

$f(x)$f(x) $=$= $-2x+3$2x+3 if $x<-4$x<4
$-3+x$3+x if $x\ge-4$x4
a

Evaluate the function when $x=-7$x=7.

b

Evaluate the function when $x=-4$x=4.

c

Evaluate the function when $x=0$x=0.

Medium
1min

Consider the function $f\left(x\right)$f(x) shown in the graph below.

Easy
2min

Consider the function $f\left(x\right)$f(x) shown in the graph below.

Easy
< 1min

The piecewise function $h\left(x\right)$h(x) is shown below:

Easy
< 1min
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Outcomes

A2.F.2

The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.

A2.F.2a

Determine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities.

A2.F.2b

Compare and contrast the characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions.

A2.F.2c

Determine the intervals on which the graph of a function is increasing, decreasing, or constant.

A2.F.2d

Determine the location and value of absolute (global) maxima and absolute (global) minima of a function.

A2.F.2e

Determine the location and value of relative (local) maxima or relative (local) minima of a function.

A2.F.2f

For any value, x, in the domain of f, determine f(x) using a graph or equation. Explain the meaning of x and f(x) in context, where applicable.

A2.F.2g

Describe the end behavior of a function.

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