Q. 17 - Precalculus Enhanced with Graphing Utilities

Question

Use the graph of the function f shown to find:

(a) The domain and the range of f 

(b) The intervals on which f is increasing,decreasing,or constant.

(c) The local minimum values and locak maximum values.

(d) The absolute maximum and absolute minimum

(e) Wheather the graph is symmetric with respect to the x-axis,y-axis,or the origin.

(f) Whether the function is even,odd or neither.

(g) The intercepts, if any.

Step-by-Step Solution

Answer

(a) The domain and range of the given function

$(-\infty ,4] and [3,-3]$ respectively.

(b) f is increasing in $(-\infty ,-2]\cup [2,4]$

     f  is decreasing in $[-2,2]$

(c)  Local minima is at $(2,-1)$

      Local maxima is at $(-2,1)$

(d)  Obsolute maxima is at $(4,3)$

      No obsolute minima for the given graph

(e)  Graph is not symmetric about x and y axises.

But,symmetric with respect to origin

(f)  It is odd function

(g) x- intercept is $(-3,0)\&(3,0)$

      y- intercept is $(0,0)$

Step 1.Given information

The given graph

Step 2.Find the domain and the range of f

From the graph,we can conclude that left horizontal exponents  of the graph is till $-\infty ,$and it terminals at $(4,3)$ on the right.

Therefore,the domain is $(-\infty ,4]$

Step 3.Find the intervals on which f is increasing,decreasing,or constant.

From the graph given in question we can see that

f  is increasing in $(-\infty ,-2]\cup [2,4]$

f  is decreasing in $[-2,2]$

Step 4.The local minimum values and local maximum values.

From the graph given in question we see that

Local minima is at $(2,-1)$

Local maxima is at$(-2,1)$

Step 5.Find the absolute maximum and absolute minimum

From the graph given  question we see that 

absolute maxima is at $(4,3)$

This graph has no absolute maxima

Step 6.Check wheather the graph is symmetric with respect to the x -axis, y -axis,or the origin.

From the graph given i question we see that Graph is not symmetric with respect to x and y axis but symmetric with respect to origin.

Step 7.Determine wheather the given function is even,odd or neither

From the graph given i question we see that 

since it is symmetric with respect to the origin.It is odd function

Step 8.Finding the intercepts, if any.

From the graph given i question we see that 

x-intercept  $(-3,0)\& (3,0)$

y-intercept $(0,0)$