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4.08 Linear absolute value 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
Easy
< 1min

Consider the graph of $y=f\left(x\right)$y=f(x) below.

Easy
1min

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

Easy
< 1min

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

Easy
1min
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Outcomes

A1.N.Q.A.1

Use units as a way to understand real-world problems.*

A1.N.Q.A.1.A

Choose and interpret the scale and the origin in graphs and data displays.*

A1.N.Q.A.1.B

Use appropriate quantities in formulas, converting units as necessary.*

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.A.CED.A.3

Create individual and systems of equations and/or inequalities to represent constraints in a contextual situation, and interpret solutions as viable or non-viable.*

A1.A.REI.D.5

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A1.A.REI.D.6

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Find approximate solutions by graphing the functions or making a table of values, using technology when appropriate.*

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.B.5

Relate the domain of a function to its graph and, where applicable, to the context of the function it models. *

A1.F.IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate and interpret the rate of change from a graph.*

A1.F.IF.C.7

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

A1.F.IF.C.9

Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.*

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.MP7

Look for and make use of structure.

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