To find:
The correct statements about the function A and the function B.
Solution:
Here, the graph of function A passes through (0, -5) and (5, -3). So, the rate of change of function A is given by:
[tex]\begin{gathered} \frac{y_2-y_1}{x_2-x_1}=\frac{-3-(-5)}{5-0} \\ =\frac{-3+5}{5} \\ =\frac{2}{5} \end{gathered}[/tex]Thus, the first statement is true.
Since, the rate of change of function A does not depend on the value of x. It is a constant value. Thus, the second statement is true.
The graph of the function A is a straight line. Therefore, the function A is linear. Thus, the third statement is true.
From the table, it is clear that the value of function B doubles when the value of x increases by 1. Thus, the fourth statement is true.
Here, the difference of the value of function B is not same with the increase in the value of x. Therefore, the rate of change of function B is not 2. Thus, the fifth statement is not true.
From the table, it is clear that the value of the function B doubles when the value of x increases by 1. Therefore, it is an exponential function. Thus, the sixth statement is true.
Thus, the first, the second, the third, the fourth, the sixth statements are true.
