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4.05 Piecewise functions

Adaptive
Worksheet

Interactive practice questions

Which of the following options describes a method for sketching a graph of $y=\left|f\left(x\right)\right|$y=|f(x)|, supposing we already have a graph of $y=f\left(x\right)$y=f(x)?

Reflect the graph of $y=f\left(x\right)$y=f(x) over the $x$x-axis.

A

Reflect the parts of the graph of $y=f\left(x\right)$y=f(x) over the $x$x-axis where $f\left(x\right)<0$f(x)<0.

B

Reflect the parts of the graph of $y=f\left(x\right)$y=f(x) over the $y$y-axis where $x<0$x<0.

C

Reflect the parts of the graph of $y=f\left(x\right)$y=f(x) over the $x$x-axis where $f\left(x\right)>0$f(x)>0.

D
Medium
< 1min

Consider the function $y=\left|3x\right|$y=|3x|.

Medium
1min

Consider the function $y=\left|x-1\right|$y=|x1|.

Medium
1min

Consider the function $y=\left|x\right|+4$y=|x|+4.

Medium
1min
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Outcomes

A.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

F.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.C.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.C.7.B

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

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