Question

Piecewise function help?

Evaluate the piecewise function at the indicated values from the domain:


| |x|, if x < = -1
f(x) = { x^2, if -1 <(or equal to) x < 4 at x = -2
| -x, if x >(or equal to) 4



(a.) f(-2) = 2
(b.) f(-2) = -4
(c.) f(-2) = -2
(d.) f(-2) = 4

Answer 1

it is hard for me to read the function and whatever else is there

Answer 2

oh it didn't show that way a sec ago

Answer 3

@freckles I just reformated it

Answer 4

now is the time to show off \(\LaTeX\) skills

Answer 5

so you want to evaluate the function at x=-2
so first of the 3 inequalities that is defined for x
which of those sets include x=-2?

Answer 6

is x=-2 in the set x<=1?
is x=-2 in the set -1<=x<4?
is x=-2 in the set x>=4?

Answer 7

another way to ask that question
is to you which inequality is true?
-2<=1?
-1<=-2<4?
-2>=4?

Answer 8

@freckles I typed it in wrong sorry, the first inequality is x < = -1, not positive.
-2 works for the first term only

Answer 9

ok when x<=-1 we will use the |x|

Answer 10

\[f(x) \left\{\begin{array}{rcc}
|x|& \text{if} & x <-1 \\
x^2& \text{if} & -1\leq x < 4\\
-x& \text{if} & x\geq 4
\end{array}
\right.
\]

Answer 11

so replace the x in |x| with -2

Answer 12

that equals positive 2, right? what next @freckles

Answer 13

that's it

Answer 14

So the answer is a, f(-2) = 2?

Answer 15

|-2|=2
f(x)=|x| when x<=-1
f(-2)=|-2|=2

Answer 16

@freckles

Answer 17

yes?

Answer 18

so is the answer a, f(-2) = 2?

Answer 19

well I was confirming your answer by saying:
|-2|=2
f(x)=|x| when x<=-1
f(-2)=|-2|=2
if it doesn't make sense what I have said, please let me know
and please tell me which part

but if you need someone to say flat out yes
Then okay

YES! :)

Answer 20

THANK YOU.