Q.28 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 21–28, the graph of a function is given. Use the graph to find:

(a) The intercepts, if any

(b) The domain and range

(c) The intervals on which it is increasing, decreasing, or constant

(d) Whether it is even, odd, or neither

Step-by-Step Solution

Answer

(a) The x -intercept point of the graph of the function is $(-2.3,0)$ and y -intercept point is $(0,1)$.

(b) The domain of graph of the function is $\left[-3,3\right]$ and range is$\left[-3,2\right]$.

(c) The graph of function is increasing on the interval $\left(-3,-2\right)\cup \left(0,2\right)$, decreasing on interval $\left(2,3\right)$ and constant in interval $\left(-2,0\right)$.

(d) Graph of the function is neither even nor odd 

Step 1. Given information

The given graph is

Step 2. Part (a)

Graph of function intersects the x-axis at Point $(-2.3,0)$

So x -intercept point is $(-2.3,0)$

Graph of function intersects the y-axis at Point $(0,1)$

So y -intercept point is $(0,1)$

Step 3. Part (b)

The graph of function state that the domain of the function is $\left[-3,3\right]$

The graph of the function state that the range of the function is$\left[-3,2\right]$

Step 4. Part (c)

The graph of the function state that the function is increasing on intervals $(-3,-2)\cup (0,2)$

The graph of the function state that the function is decreasing on intervals $(2,3)$

The graph of the function state that the function is constant on intervals $(-2,0)$.

Step 5. Part (d)

The graph of the function is neither symmetric with respect to the y-axis nor symmetric with respect to the origin.

So Graph of the function is neither even nor odd.