Question

Use the graph off the function g to answer the following questions.

Answer 1

2.

Observe the given graph carefully.

(a)

The value of g(-3) is the image of point x = -3.

This is seen as the y coordinate of the point that corresponds to x=-3.

From the figure, this point is seen as,

$(-3,-1)$

Thus, the required value is,

$g(-3)=-1$

(b)

It is asked to find all the values of 'x' such that,

$g(x)=-3$

This refers to all the points on the curve whose y-coordinates is -3.

From the graph, those points are evident as,

$(-2,-3)\text{ and }(0,-3)$

So the points x=-2 and x=0 both correspond to g(x)=-3.

Thus, the required values of 'x' are,

$-2,0$

(c)

The range of a function is the set of all values that the function can take. It is observed by the values on y-axis that the graph of the function takes.

Observe that the function takes all values between -5 and 3, including the end-point -5 but not 3.

Thus, the range of the function in interval notation can be expressed as,

$-5\leq g(x)<3$

Or this same range can also be represented using braces as,

$\lbrack-5,3)$