Question

what is the value of f(-2)
f(x)= -2 if x<-3
4x if -3<(equal to) x <( equal to) -1
x^2 if x>-1
a.-8
b.4
c-2
d8

Answer 1

So for f(-2), x = -2. Which of those criteria (if x <-3, -3<_x<_-1, and -1<x) does x=-2 fall under in this piecewise function?

Answer 2

the first one?

Answer 3

-2 is x <-3?

Answer 4

No, -2 is actually -3<_x<_-1. When x = -2, it is greater than -3 and less than -1.

Do you understand this?

Answer 5

yes now i do thank you

Answer 6

it always helps to graph the piece wise equations.
What is f(x) or y when x is less than -3 ? y = -2 for every x less than 2
What is f(x) or y when x is equal to or between -3 and -1 ? y = 4x for the stated domain
What is f(x) or y when x is greater than -1 ? y = x^2 for every x greater than -1

Answer 7

x f(x) domain
-10 -2 f(x)=-2 for x<-3
-9 -2 f(x)=-2 for x<-3
-8 -2 f(x)=-2 for x<-3
-7 -2 f(x)=-2 for x<-3
-6 -2 f(x)=-2 for x<-3
-5 -2 f(x)=-2 for x<-3
-4 -2 f(x)=-2 for x<-3
-3 -12 f(x)=4x for -3 <= x <= -1
-2 -8 f(x)=4x for -3 <= x <= -1
-1 -4 f(x)=4x for -3 <= x <= -1
0 0 f(x)=x^2 for x > -1
1 1 f(x)=x^2 for x > -1
2 4 f(x)=x^2 for x > -1
3 9 f(x)=x^2 for x > -1
4 16 f(x)=x^2 for x > -1
5 25 f(x)=x^2 for x > -1
6 36 f(x)=x^2 for x > -1

I think it would look like this (roughly)