Question

Using the graph of the function $f$:

(a) Find the domain and the range of $f$.

(b) List the intercepts.

(c) Find $f\left(1\right)$.

(d) For what value(s) of $x$does $f\left(x\right)=-3$?

(e) Solve $f\left(x\right)<0$.

Short answer

(a) Domain is $x\in [-5,5]$

Range is $y\in [-3,3]$

(b) $x$-intercepts are $(-2,0)$and $(2,0)$

$y$-intercept is $(0,2)$

(c) $f\left(1\right)=3$

(d) $f\left(x\right)=-3$at $x=-5$and $x=3$

(e) $f\left(x\right)<0$forrole="math" localid="1645962870014" $x\in [-5,-2)\cup (2,5]$

Step-by-step solution

Step 1. Part (a) Find the domain and the range of f.

By looking at the graph,

Domain is $x\in [-5,5]$

Range is$y\in [-3,3]$

Step 2. Part (b) List the intercepts.

By looking at the graph,

$x$-intercepts are $(-2,0)$and $(2,0)$

y-intercept is$(0,2)$

Step 3. Part (c) Find f(1)

By looking at the graph,

$f\left(1\right)=3$

Step 4. Part (d) Find values of x for which f(x)=-3.

By looking at the graph,

$f\left(x\right)=-3$at role="math" localid="1645962742345" $x=-5,3$

Step 5. Part (e) Solve f(x)<0.

By looking at the graph,

$f\left(x\right)<0$ is for$x\in [-5,-2)\cup (2,5]$