Question

Given the piecewise function shown below, select all of the statements that are true.
A. f(4)=7
B. f(-2)=0
C. f(1)=0
D. f(-1)=2

Answer 1

well, let's check each answer choice

Answer 2

if x = 4, what does f(x) = ?

Answer 3

f(4)?

Answer 4

yes, but what does that equal?

Answer 5

f(4) = ?

Answer 6

I dont know

Answer 7

look at the function

Answer 8

there are three rows

Answer 9

Yes

Answer 10

For the first row it would be -4+1,4<0. Right?

Answer 11

-x + 1 , x<0 means that f(x) = -x+1 only when x is less than 0
-2, x = 0 means f(x) = -2 when x = 0
x^2 - 1, x > 0 means that f(x) = x^2 - 1, only when x > 0

Answer 12

so , if x = 4, which row should we use?

Answer 13

The last

Answer 14

good!

so if x = 4, what does x^2 - 1 = ?

Answer 15

17?

Answer 16

almost

Answer 17

4^2 - 1 = ?

Answer 18

Oh. Im sorry

Answer 19

15

Answer 20

great! so f(4) = 15

now we check the first answer choice

it says f(4) = 7, so A must be false

Answer 21

what about x = -2? which row do we use?

Answer 22

The top

Answer 23

great!

so if x = -2, what is -x + 1?

Answer 24

-1

Answer 25

almsost

Answer 26

-(-2) + 1 = ?

Answer 27

3?

Answer 28

good

so B must also be false since f(-2) is 3 and not 0

Answer 29

what about x = 1? which row?

Answer 30

The third

Answer 31

great!

so if x = 1, what is x^2 - 1?

Answer 32

0

Answer 33

fantastic!

so C must be true

Answer 34

last one

what about x = -1? which row?

Answer 35

The top

Answer 36

good

so if x = -1, what is -x + 1?

Answer 37

2

Answer 38

fantastic

so D must also be true

Answer 39

C and D are your answers

Answer 40

great work

Answer 41

Thanks a bunch. I really appreciate it.