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)=1/2x−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

m = rate of change of the functions.

1) m = 1/2

2) m = -1

3) m = -2

4) m = 1

5) m = 2

Explanation:

Hi there!

For the points (a, f(a)) and (b, f(b)), the rate of change between them, m, is calculated as follows:

m = f(b) - f(a) / (b - a)

Then:

1) f(x) = 1/2 x - 3

f(0) = 1/2 · 0 -3 = -3

f(6) = 1/2 · 6 - 3 = 0

m = f(6) - f(0) /( 6 - 0)

m = 0 - (-3) / 6 = 1/2

2) f(x) = -x

f(-4) = -(-4) = 4

f(2) = -2

m = f(2) - f(-4) /(2 - (-4)

m = -2 - 4 / 2 + 4

m = -6/6

m = -1

3) f(x) = x²

f(-2) = (-2)² = 4

f(0) = 0² = 0

m = f(0) - f(-2) / 0 - (-2)

m = 0 - 4/ 2 = -2

4) f(x) = x³

f(-1) = (-1)³ = -1

f(1) = 1³ = 1

m = f(1) - f(-1) / 1 - (-1)

m = 1 - (-1)/ 2

m = 2/2 = 1

5) f(x) = 2x

f(0) = 2 · 0 = 0

f(4) = 2 · 4 = 8

m = f(4) - f(0) / (4 - 0)

m = 8 - 0 / 4

m = 2