Question

Evaluate the function for the indicated values of x.

Answer 1

In the explanation:

Explanation:

f(-10) means we need to find the piece so that x is also satisfied.

So we have x=-10 here. Which of your pieces satisfy that?

Well
`-10 \le -5` so the first piece.

`f(-10)=2(-10)+1=-20+1=-19`.

f(2) means we find the piece so that x is also satisfied.

So we have x=2 here. Which of your pieces satisfy that?

Well
`-5<2<5` so the second piece.

`f(2)=(-2)^2=4`.

f(-5) means we use the piece that satisfied x=-5.

-5 equals -5 and the equals -5 part is included in the first piece.

`f(-5)=2(-5)+1=-10+1=-9`

f(-1) means use the piece so that x=-1 is satisfied.

-1 is between -5 and 5 so use
`x^2`

`f(-1)=(-1)^2=1`

f(8) means use the piece so that x=8 is satisfied.

9 is greater than 5 so we use the third piece.

`f(8)=3-8=-5`

It looks like you have all the answers and you are trying to figure out why.

Let's do another problem.

What piece would you use if I asked you to evaluate:

f(-2)?

x=-2 satisfies the
`-5<x<5` so we use the
`x^2`

`f(-2)=(-2)^2=4`

f(-6)?

x=-6 satisfies the
`x \le -5` so we use the
`2x+1`

`f(-6)=2(-6)+1=-12+1=-11`

f(7)?

x=7 satisfies
`x \ge 5` so we use
`3-x`

`f(7)=3-7=-4`

I will post the answers here after you had time to think about it.

Answer 2

`f( - 10) = 2(-10)+1`

which is then equal to-19

`f(2)=2^2 \\`

which is then equal to 4

`f(-1)=1^2 \\`

which is then equal to 1

`f(8)=3-8 \\`

which is then equal to -5