Question

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

Answer 1

Step 1 :

(a)

Find - intercept :

- intercept : The point where .

Observe the graph for - intercept.

The - intercepts are and .

Find - intercept :

- intercept : The point where .

Observe the graph for - intercept.

The - intercept is .

Step 2 :

(b)

All possible values of is the domain of a function.

The domain is or .

Range is the corresponding values of the function for different values of .

The range is or .

Solution :

(a) - intercepts : and and - intercept : .

(b) The domain is or .

     The range is or .

Answer 2

Step 1 :

(c)

The function is increasing for all values of between to and to .

The function is increasing over the interval and .

The function is decreasing for all values of between to and to .

The function is decreasing over the interval and .

Step 2 :

(d)

If the graph is symmetric about - axis, then it is an even function.

If the graph is symmetric about origin, then it is an odd function.  

The graph is symmetric about - axis, thus it is an even function.

Solution :

(c) The function is increasing over the interval and .

    The function is decreasing over the interval and .

(d) Even.