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

Short 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 role="math" localid="1647284294310" $\left(-2,0\right)$.

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

Step-by-step solution

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.