# How do you graph, find the zeros, intercepts, domain and range of f(x)=abs(4x)?

##### 1 Answer
Feb 20, 2017

Graph: A straight line from the origin of slope 4, with a miror reflection about the $y$ axis.
$f \left(0\right) = 0$, Domain: $\left(- \infty , + \infty\right)$, Range: $\left(0 , + \infty\right)$

#### Explanation:

$f \left(x\right) = \left\mid 4 x \right\mid$

$f \left(x\right) = 4 x$ for $x > 0$ [A straight line from the origin of slope 4]
and
$f \left(x\right) = - 4 x$ for $x < 0$ [A straight line from the origin of slope -4]
and
$f \left(x\right) = 0$ for $x = 0$ [The single zero and intercept of $f \left(x\right)$]

$f \left(x\right)$ is defined $\forall x \to$ The domain of $f \left(x\right)$ is $\left(- \infty , + \infty\right)$

$f \left(x\right) \ge 0 \forall x \to$ The range of $f \left(x\right)$ is $\left(0 , + \infty\right)$

These can be seen from the graph of $f \left(x\right)$ below:

graph{abs(4x) [-11.21, 11.29, -2.145, 9.105]}