Q. 5 - Precalculus Enhanced with Graphing Utilities

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

Step-by-Step Solution

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

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 $x=-5,3$

Step 5. Part (e) Solve f ( x ) &#60; 0 .

By looking at the graph,

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