Question

Linear function A and linear function B both have the same input values as shown below. Why will the output values for

linear function A always be different than the corresponding output values for linear function B?
Linear Function A
Linear Function B
y
3
y У
4
8
х
1
3
5
7
9
11
15
19
х
1
3
5
7
9
16
20

a) The initial values of the two functions are different, and the rates of change of the two functions are also different.
b) The initial values of the two functions are different, and the rates of change of the two functions are the same.
c) The initial values of the two functions are the same, and the rates of change of the two functions are different.
d) The initial values of the two functions are the same, and the rates of change of the two functions are also the same.

Answer 1

The output values for linear function A will always be different than the corresponding output values for linear function B because the initial values and rates of change for the two functions are different.

Step-by-step explanation:

The correct answer is a) The initial values of the two functions are different, and the rates of change of the two functions are also different.

Linear Function A and Linear Function B have different initial values and different rates of change, which is why their output values will always be different. The initial values represent the y-intercepts of the functions, where they intersect the y-axis. The rates of change, or slopes, represent how much the y-value changes for each unit increase in the x-value. Since the initial values and rates of change are different for Linear Function A and Linear Function B, their output values will also be different.

Answer 2

The initial values of the two functions are different, and the rates of change of the two functions are also different The correct answer is (a) .

Step-by-step explanation:

Linear functions are characterized by their initial values (y-intercept) and rates of change (slope). In this scenario, the given functions are denoted as yₐ and yᵦ with corresponding input values x. The initial values are indicated by the values of yₐ and yᵦ when x = 1. In function A, yₐ = 3, whereas in function B, yᵦ = 4. Since these initial values differ, the functions start at different points on the y-axis.

Additionally, the rates of change can be determined by observing the differences in the output values for consecutive input values. Taking x = 1 to x = 3, the change in yₐ is 8 - 3 = 5, while the change in yᵦ is 16 - 4 = 12. This demonstrates that the rates of change for functions A and B are different.

Therefore, the correct choice is (a) – the initial values are different, and the rates of change also differ. This distinction in starting points and rates of change guarantees that the output values for linear function A will consistently differ from the corresponding output values for linear function B The correct answer is (a) .