Question

Which linear function below is increasing at the fastest rate?

A (x)
B (x)
C (x)
D (x)

Answer 1

Step 1 :

The rate of change of a function between any 2 points x1,x2 is calculated using the formula m = (f(x2) -f(x1)) /(x2 - x1 )

Also the function which has the highest rate of change increases at the fastest rate.

Step 2:

We will find the rate of change of all the functions between any 2 points

Rate of change of a(x) = (5 - (-5))/((1.5-(-1.5)) = 10/3

Rate of change of b(x) = (5 - (-5))/((5-(-5)) = 10/10 =1

Rate of change of c(x) = (2.5 - (-2.5))/((5-(-5)) = 5/10

Rate of change of d(x) = (1 - (-1))/((5-(-5)) = 2/10

Here we see that the function a(x) has the highest rate of change and hence has increases at the fastest rate.

Explanation:

Answer 2

Explanation:

Step 1 :

The rate of change of a function between any 2 points x1,x2 is calculated using the formula m = (f(x2) -f(x1)) /(x2 - x1 )

Also the function which has the highest rate of change increases at the fastest rate.

Step 2:

We will find the rate of change of all the functions between any 2 points

Rate of change of a(x) = (5 - (-5))/((1.5-(-1.5)) = 10/3

Rate of change of b(x) = (5 - (-5))/((5-(-5)) = 10/10 =1

Rate of change of c(x) = (2.5 - (-2.5))/((5-(-5)) = 5/10

Rate of change of d(x) = (1 - (-1))/((5-(-5)) = 2/10

Here we see that the function a(x) has the highest rate of change and hence has increases at the fastest rate.