Question

1 Two functions are shown below. Function A Function B x 0 3 5 y 5 3x 1 2 y 3 9 13 Which statement correctly describes the rates of change of the two functions? A The rate of change is 2 for both Function A and Function B. B The rate of change is 3 for both Function A and Function B. C The rate of change is greater for Function A than for Function B. D The rate of change is greater for Function B than for Function A.

Answer 1

D The rate of change is greater for Function B than for Function A

Explanation:

A function shows the relationship between a dependent variable and an independent variable. A linear function is given as y = mx + b, where m is the rate of change, y is the dependent variable, x is the independent variable and b is the value of y when x = 0.

Function B is given by y = 3x + 2. Comparing with y =mx + b gives m = 3. Therefore the rate of change of function B is 3.

Function A has x: 0, 3, 9 and y:3, 9, 13. Using the points (0,3) and (3, 9), we an get the equation of the function. The formula is:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)\\\\y-3=(9-3)/(3-0)(x-0)\\ \\y-3=2x\\\\y=2x+3`

Function A is given by y = 2x + 3. Comparing with y =mx + b gives m = 2. Therefore the rate of change of function A is 2.

The rate of change is greater for Function B than for Function A