Question

(a) Find h(- 2), h(0), h(2) , and h(3) (b) Find the domain and range of h.(c) Find the values of x for which h(x) = 3 .(d) Find the values of x for which h(x) <= 3 .(e) Find the net change in h between x = - 3 and x = 3 .УА3h-303X

Answer 1

#7

(a)

To find values of the function h at different x values, we go straight to that x value and find the corresponding y value of the graph.

From the graph, we have:

`\begin{gathered} h(-2)=1 \\ h(0)=-1 \\ h(2)=3 \\ h(3)=4 \end{gathered}`(b)

The domain of a function is the set of x-values for which the graph of the function is defined.

The range of a function is the set of y-values for which the graph of the function is defined.

Looking at the graph, we see that from

x = - 3 to x = 4, the function is defined.

Also, from

y = - 1 to y = 4, the function is defined.

Thus, we can write the domain and range as >>>>>

`\begin{gathered} D=-3\leq x\leq4 \\ R=-1\leq y\leq4 \end{gathered}`

(c)

h(x) = 3 means y = 3

We will draw a horizontal line at y = 3 and see the points at which that line and curve crosses. Then, we will draw a perpendicular from that point to the x-axis. These are the values of x for which y = 3.

The graph:

We see from the graph drawn that for x = - 3, x = 2, and x = 4, the value of the function h is 3.

So,

`x=-3,2,4`

(d)

The values of x for which the function is ≤ 3 can be found by again drawing a line y = 3 and finding the places where the graph is BELOW that line.

Graph:

So, we can see that from x = - 3 to x = 2, the function is less than or equal to 3.

Thus,

`-3\leq x\leq2`

(e)

From x = - 3 to x = 3, the function changes several values. But the net change can be found by finding the respective values of the function at x = - 3 and at x = 3 and finding the difference.

At x = - 3, the function has a value of "3".

At x = 3, the function has a value of "4".

Thus, the net change is 4 - 3 = 1

Net Change = 1