Question

Which statement about the properties of Function A and Function B are true?

Select each correct statement.
A The Y-intercept of Function A is equal to the Y-intercept of Function B.
B The Y-intercept of Function A is less than the Y-intercept of Function B.
The Y-intercept of Function A is greater than the Y-intercept of Function B.
D The rate of change of Function A is equal to the rate of change of Function B.
E The rate of change of Function A is less than the rate of change of Function B.

Answer 1

B. The Y-intercept of Function A is less than the Y-intercept of Function B

F. The rate of change of Function A is greater than the rate of change of Function B

Explanation:

Function A rate of change and y-intercept:

✔️Rate of change using two pairs of values from the given table, (1, 2) and (3, 10):

Rate of change = ∆y/∆x = (10 - 2) / (3 - 1) = 8/2 = 4

Rate of change (m) of Function A = 4

✔️ To find the y-intercept (b) of function A, substitute (x, y) = (1, 2) and m = 4 into y = mx + b (slope-intercept form):

2 = 4(1) + b

2 = 4 + b

2 - 4 = b

-2 = b

b = -2

Y-intercept (b) of function A = -2

Function B rate of change (m) and y-intercept (b):

The function, y = 3x + 4 is given in the slope-intercept form, y = mx + b.

Therefore,

Rate of change/slope (m) = 3

Y-intercept (b) = 4

The following staments about the properties of both functions are therefore true:

B. The Y-intercept of Function A is less than the Y-intercept of Function B

F. The rate of change of Function A is greater than the rate of change of Function B