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4.09 Transforming absolute value functions

Adaptive
Worksheet

Interactive practice questions

How do we shift the graph of $y=f\left(x\right)$y=f(x) to get the graph of $y=f\left(x\right)+4$y=f(x)+4?

Move the graph up by $4$4 units.

A

Move the graph down by $4$4 units.

B
Easy
< 1min

How do we shift the graph of $y=g\left(x\right)$y=g(x) to get the graph of $y=g\left(x+6\right)$y=g(x+6)?

Easy
< 1min

Suppose that the $x$x-values of the $x$x-intercepts of the graph of $y=f\left(x\right)$y=f(x) are $-5$5 and $6$6.

Medium
4min

The table below shows values that satisfy the function $f\left(x\right)=\left|x\right|$f(x)=|x|.

Hard
4min
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Outcomes

A1.A.CED.A.2

Create equations in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.*

A1.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.*

A1.F.IF.C.7

Graph functions expressed algebraically and show key features of the graph by hand and using technology.*

A1.F.BF.B.2

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given graphs.

A1.MP1

Make sense of problems and persevere in solving them.

A1.MP3

Construct viable arguments and critique the reasoning of others.

A1.MP6

Attend to precision.

A1.MP8

Look for and express regularity in repeated reasoning.

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