iGCSE (2021 Edition)

# 4.07 Absolute value functions

## 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

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

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

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

### Outcomes

#### 0606C1.3

Understand the relationship between y = f(x) and y = |f(x)|, where f(x) may be linear, quadratic or trigonometric.

#### 0606C2.3

Know the conditions for f(x) = 0 to have two real roots, two equal roots, no real roots. Know the related conditions for a given line to intersect a given curve, be a tangent to a given curve, not intersect a given curve.

#### 0606C2.4B

Find the solution set for quadratic inequalities.