Answer:
In the explanation:
Step-by-step 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 [tex]-10 \le -5[/tex] so the first piece.
[tex]f(-10)=2(-10)+1=-20+1=-19[/tex].
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 [tex]-5<2<5[/tex] so the second piece.
[tex]f(2)=(-2)^2=4[/tex].
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.
[tex]f(-5)=2(-5)+1=-10+1=-9[/tex]
f(-1) means use the piece so that x=-1 is satisfied.
-1 is between -5 and 5 so use [tex]x^2[/tex]
[tex]f(-1)=(-1)^2=1[/tex]
f(8) means use the piece so that x=8 is satisfied.
9 is greater than 5 so we use the third piece.
[tex]f(8)=3-8=-5[/tex]
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 [tex]-5<x<5[/tex] so we use the [tex]x^2[/tex]
[tex]f(-2)=(-2)^2=4[/tex]
f(-6)?
x=-6 satisfies the [tex]x \le -5[/tex] so we use the [tex]2x+1[/tex]
[tex]f(-6)=2(-6)+1=-12+1=-11[/tex]
f(7)?
x=7 satisfies [tex]x \ge 5[/tex] so we use [tex]3-x[/tex]
[tex]f(7)=3-7=-4[/tex]
I will post the answers here after you had time to think about it.
