Absolute Value Functions

Consider the graph of the function $f\left(x\right)$`f`(`x`).

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a

State the coordinate of the vertex.

b

State the equation of the line of symmetry.

c

What is the gradient of the function for $x>0$`x`>0?

d

What is the gradient of the function for $x<0$`x`<0?

e

Hence, which of the following statements is true?

The graph of $f\left(x\right)$`f`(`x`) is steeper than the graph of $y=\left|x\right|$`y`=|`x`|.

A

The graph of $f\left(x\right)$`f`(`x`) is not as steep as the graph of $y=\left|x\right|$`y`=|`x`|.

B

The graph of $f\left(x\right)$`f`(`x`) has the same steepness as the graph of $y=\left|x\right|$`y`=|`x`|.

C

The graph of $f\left(x\right)$`f`(`x`) is steeper than the graph of $y=\left|x\right|$`y`=|`x`|.

A

The graph of $f\left(x\right)$`f`(`x`) is not as steep as the graph of $y=\left|x\right|$`y`=|`x`|.

B

The graph of $f\left(x\right)$`f`(`x`) has the same steepness as the graph of $y=\left|x\right|$`y`=|`x`|.

C

Easy

Approx 2 minutes

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Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

Apply graphical methods in solving problems