Question

The graph of a piece-wise defined function is given. Write a definition for the function that best describes this graph.
**open to see graph**

Answer 1

@jim_thompson5910 here's the question

Answer 2

you essentially have 2 linear equations being combined here

Answer 3

so the idea is to find the equation of each piece

Answer 4

what is the equation of the left piece?

Answer 5

no clue

Answer 6

what points lie on this left line?

Answer 7

(-3,2),(0,0)

Answer 8

what is the slope of the line that goes through those two points

Answer 9

3/-2?

Answer 10

incorrect

Answer 11

sorry -2/3

Answer 12

better

Answer 13

what is the y-intercept of that line?

Answer 14

0?

Answer 15

so the equation of that left piece is

\[\Large y = -\frac{2}{3}x + 0\]

which turns into

\[\Large y = -\frac{2}{3}x\]

Answer 16

it is only defined when x is between -3 and 0

ie when \[\Large -3 \le x \le 0\]

Answer 17

so the answer would be f(x)=-2/3 if −3≤x≤0

Answer 18

\[\Large y = -\frac{2}{3}x\] not just -2/3

Answer 19

but yeah with that condition on x

Answer 20

hopefully you see how to do the other piece

Answer 21

is is the same way?

Answer 22

yes pretty much

Answer 23

same method, just different points

Answer 24

ok!! thank you!

Answer 25

could you help me with one more problem please?

Answer 26

sure

Answer 27

If f(x)=int (4x),find:
(a.) f(2.7)
(b.) f(2.2)
(c.)f (-2,8)

Answer 28

the int function just has you round down to the nearest integer

examples

int(3.2) = 3
int(4.7) = 4
int(6.8) = 6
int(-7.1) = -8

one thing to note: you do NOT go from -7.1 to -7, you would head down to the nearest integer which is -8. I think to think of it as you place the number line vertically and you head down to the floor of the next number.

something like this http://www.pearsoned.ca/highered/divisions/economics/images/Fg_-03.gif

Answer 29

I did what you said...but it says i'm incorrect?

Answer 30

what did you get for each

Answer 31

i got 8 for the first one...cause i rounded down 2.7 to 2 and plugged that in for x

Answer 32

f(x) = int (4x)

f(2.7) = int (4*2.7)

f(2.7) = int (10.8)

f(2.7) = 10

Answer 33

you round after you multiply

Answer 34

because you do the inner stuff first in the parenthesis, then move onto the outer stuff

Answer 35

oh ok let me try that

Answer 36

it worked thankyou!!!

Answer 37

ok great