Question

The function f(x) is represented by this table of values.

Answer 1

theres the rest of the quetion...

Answer 2

*question. so do i have to do that for each?

Answer 3

yeah
so figure out the change over the interval
[a,b] = [-5,-1]

Answer 4

ill start typing it up.

Answer 5

i know i did something wrong again...for the first i got 6/5

Answer 6

Interval [a,b] = [-5,-1]

values f(a) = f(-5) = 35
f(b) = f(-1) = 3

Rate of change
\[slope = \frac{ f(b) - f(a) }{ b - a } = \frac{ f(-1) - f(-5) }{ -1 - (-5) } = \frac{ 3 - 35 }{ -1 - (-5) }= \frac{ -32 }{ 4 } = -8\]

Answer 7

see what you did wrong?

Answer 8

kind of...

Answer 9

Conceptually, all we are doing is finding a fraction of the difference in 'y' values, divided by the difference in 'x' values. Where y = f(x)

Answer 10

i'm confused with the negative one...where did that come from?

Answer 11

i understand the last comment / response you had,...i know what we're trying to find but am having troubling solving/ setting up

Answer 12

for the interval
[a,b] = [-5,-1] (x-values)
and
f(-5) = 35 ; f(-1) = 3 (y-values)

Answer 13

difference in y values is f(-1) - f(-5)
difference in x values is... (-1) - (-5) = -1 + 5 = 4

Answer 14

minus a negative means plus... like

10 - (-3) means
10 + 3

Answer 15

i'm taking notes:) doing my best to follow yah!! can we try the nesxt?

Answer 16

*next

Answer 17

Ok, for the second interval

[a,b] = [-4,-1]
Type out each step individually

Answer 18

What is the first thing to do?

Answer 19

change over the interval?

Answer 20

First thing, write down what f(x) is at both those endpoints.

Answer 21

24, 3 ?

Answer 22

yes, but keep it in this form

f(-4) = 24
f(-1) = 3

Answer 23

now use this
\[\frac{ f(-1) - f(-4) }{ -1 - (-4) }\]

Answer 24

\[-4-(-11)/24-3 \]

Answer 25

never mind. it's a negative one, not eleven.

Answer 26

still you have it upside down

Answer 27

look at the formula again

Answer 28

21/ -3 ...does that look better?

Answer 29

\[\frac{ f(-1) - f(-4) }{ -1 - (-4) } = \frac{ 3 - 24 }{ -1 + 4 }\]

Answer 30

that reduces to -21/3 ...correct?

Answer 31

which then is -7 ?

Answer 32

all you have to do is match up numbers,
[a,b] =[-4,-1]
f(a) =24
f(b) = 3

\[\frac{ f(b) - f(a) }{ b - a }\]

Answer 33

yeah -7 , correct

Answer 34

Third one
write everything out like this

[a,b] = [-3,1]
f(a) =
f(b) =

\[\frac{ f(b) - f(a) }{ b - a }\]