Question

Find the domain and range of h(x)

Answer 1

the domain is the possible values of x
range is the values of y
the shaded circles indicate that these values are inclusive

Answer 2

can you clarify a little more?

Answer 3

The domain is the possible values for x. Since the function is continuous, it's simply from the furthest left x, to the furthest right x. Shaded circles means it includes that value. The range is the same as the domain, except you're dealing with y. What are the smallest and largest values of y?

Answer 4

smallest is -2 and largest is 2?

Answer 5

That would be your range, yes. Because those are the smallest and largest values of y. Bear in mind, this is because the function is continuous (no holes, steps, breaks, asymptotes, etc...)

Answer 6

So, the range is (-inf,-2] U [2,inf) ?

Answer 7

No, you have it backwards. You have everything that is NOT in the graph with that interval.

Answer 8

backwards? [-2,-inf) U (inf,2] ?

Answer 9

No :) You have everything that is NOT in the graph. In this notation, your range is simply:
\[[-2, 2]\]

Answer 10

So, -2 and 2 is not in the graph?

Answer 11

What the interval [-2, 2] is saying is that the range includes all real numbers between -2 and 2, including both of them.

Answer 12

the [] means "inclusive", and () means exclusive.

Answer 13

ohh.. okay. isn't the domain exactly opposite?

Answer 14

-3 and 3?

Answer 15

The domain does the same, just on 'x', not 'y'. Here that is correct, your domain goes from -3 to 3

Answer 16

(and includes them both)

Answer 17

[-3,3] ?

Answer 18

That's correct.

Answer 19

now, how do I find the corresponding functions for h(1), h(3), h(-1), and h(2)?

Answer 20

This is h(x), essentially what this means is substitute those numbers in for x. So, for h(1), just follow the x axis over to 1, and see what the corresponding y-value is.

Answer 21

h(1)= 0

Answer 22

That's correct, just repeat the process for the other values.

Answer 23

okay :) thank you!

Answer 24

Np.