Question

For each function, use the slope formula to calculate the rate of change between the points. In your final answer, include all of your calculations.

f(x):

(a, f(a) and (b,f(b)

1.) f(x)=x - 3 (0,f(0)) and (6,f(6))
2.) f(x) = -x (-4,f(-4)) and(2,f(2))
3.) f(x)=x2 (-2,f(-2)) and (0,f(0))
4.) f(x)=x3 (-1,f(-1)) and (1,f(1))
5.) f(x)=2x (0,f(0)) and (4,f(4))

Answer 1

Function 1:

f(x) = x - 3
f(0) = 0 - 3 = -3
f(6) = 6 - 3 = 3

Slope =
`(-3-3)/(6-0) = (-6)/(6) =-1`

Function 2:

f(x) = -x
f(-4) = 4
f(2) = -2

Slope =
`(4--2)/(-4-2)= (6)/(-6)=-1`

Function 3:

f(x) = x²
f(-2) = (-2)² = 4
f(0) = (0)² = 0

Slope =
`(4-0)/(-2-0)= (4)/(-2)=-2`

Function 4:

f(x) = x³
f(-1) = (-1)³ = -1
f(1) = (1)³ = 1

Slope =
`(-1-1)/(-1-1)= (-2)/(-2)=1`

Function 5:

f(x) = 2ˣ
f(0) = 2⁰ = 1
f(4) = 2⁴ = 16

Slope =
`(1-16)/(0-4)= (-15)/(-4)=3.75`