Question

Compare the functions shown below:

What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = -1 to x = 3?

Answer 1

i know the average rate of change means slope .. and it's y2-y1/x2-x1 .. and i have calculated the slope for each on from x=-1 to x=3 and the slope for
g(x) = 0
h(x) = 12
f(x) = 0 ( and it's where i'm struggling on because it only has aproximetley x= -1.5 from x=-1 and to x=3 it doesn't exist ) how to calculate slope for it?

Answer 2

@rational @hartnn @Loser66 @ElonaSushchik @SyedMohammed98

Answer 3

is x=3 for f(x) =o because on the graph it doesn't exist?

Answer 4

h(x)

x y
-3 2
-2 7
-1 14
0 23
1 34
2 47
3 62

Answer 5

f(x) = (x + 3)^2 - 2

Answer 6

and g(x) is in the picture that i uploaded

Answer 7

@Zebrasandsparkles914 @mathmath333 @peachpi @puppylover0617 @Maretch @mathmath333 @math92130

Answer 8

@amistre64

Answer 9

@Preetha

Answer 10

ok, so you know we need slope, but i dont see your functions, only h(x)

Answer 11

g(x) is the picture

Answer 12

f(x) is posted as an equation .... ok found them all

Answer 13

the slope of g(x) is not 0, a slope of 0 gives a horizontal (flat) line.

what is the slope of the line i the picture?

Answer 14

the slope for h(x) is good, its 12

Answer 15

since the difference in x is the same for each calculation of slope (3--1) = 4 then the greatest change of y is what determine the rate of change.

calculate the values of

f(3) - f(1)

g(3) - g(1)

h(3) - h(1)

and order them

Answer 16

-1s not 1s

Answer 17

f(3) - f(-1)

g(3) - g(-1)

h(3) - h(-1)

thats better

Answer 18

sorry the slope for g(x) which is in the picture is wrong the points are (-1,-2) , (3,0) i had the first point (-1,0) by mistake so the slope for g(x) is = .5

Answer 19

good, 1/2 or in the case of just y parts:

g(3) - g(-1) = 2

Answer 20

h(3) - h(-1) = 48

what is f(3) - f(-1) ?

Answer 21

but when i graph f(x) i don't see points from x= -1 to 3 it's only x=-1.5 and it continues there .. so how to calculate the slope for it?

Answer 22

dont graph it, calculate it

Answer 23

how? what do you mean

Answer 24

f(3) - f(-1)

what is it?

Answer 25

4

Answer 26

f(x) = (x + 3)^2 - 2

f(a) = (a + 3)^2 - 2
f(b) = (b + 3)^2 - 2

f(a) - f(b) = (a+3)^2 - (b+3)^2 -2+2
| =0 |

(3+3)^2 - (-1+3)^2

9^2 - 2^2 is not 4

Answer 27

f = 77/4

g = 2/4

h = 48/4

since all of them have a denominator of 4, the top parts define their relative sizes

Answer 28

by the way, you correctly stated that slope is calculated as:

(y2-y1)/(x2-x1)

but then you state this: "when i graph f(x) i don't see points from x= -1 to 3 it's only x=-1.5 and it continues there .. so how to calculate the slope for it"

what good is it to know the formula, if you dont know how to apply it?

Answer 29

f(3) - f(-1)
--------- = slope of f between x=3 and x=-1
3 - -1

Answer 30

i tried to graph it so i can plug in the points from the interval x=-1 to x=3 but i didn't see it .. but thank you i understand now that i have to plug in -1 and 3 and then solve with the formula.

Answer 31

it does make life less labor intensive :) plotting is fine, but it has its limitations.

Answer 32

so i plug in f(3) and f(-1) in the equation and then the answers i plug them back in y2-y1/x2-x1 correct?

Answer 33

yes

Answer 34

thank you very much .. i appreciate you! @amistre64

Answer 35

youre welcome