Absolute Value Functions

NZ Level 7 (NZC) Level 2 (NCEA)

Identify Characteristics of Absolute Value Functions II

Consider the function $f\left(x\right)=\left|x\right|$`f`(`x`)=|`x`| that has been graphed. Notice that it opens upwards.

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a

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

b

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

c

The graph below shows the graph of $y$`y` that results from reflecting $f\left(x\right)$`f`(`x`) about the $x$`x`-axis. State the equation of $y$`y`.

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d

Select all the correct statements.

A downward absolute value function goes from decreasing to increasing.

A

An upward absolute value function goes from decreasing to increasing.

B

An upward absolute value function goes from increasing to decreasing.

C

A downward absolute value function goes from increasing to decreasing.

D

A downward absolute value function goes from decreasing to increasing.

A

An upward absolute value function goes from decreasing to increasing.

B

An upward absolute value function goes from increasing to decreasing.

C

A downward absolute value function goes from increasing to decreasing.

D

Easy

Approx 3 minutes

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