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Given [tex]f(a) = 71 + 72a[/tex], answer the following:

1. Average rate of change [tex]= \square[/tex]

2. [tex]f(a)[/tex]-intercept [tex]= \square[/tex]

Answer :

To solve the problem and find the requested values, let's go through each part step-by-step:

1. Average Rate of Change:
- The function [tex]\( f(a) = 71 + 72a \)[/tex] is a linear function. In a linear function like this, the average rate of change is constant and equal to the coefficient of the variable [tex]\( a \)[/tex], which is the number multiplying [tex]\( a \)[/tex].
- Here, the coefficient of [tex]\( a \)[/tex] is 72. So, the average rate of change is 72.

2. [tex]\( f(a) \)[/tex]-Intercept:
- To find the [tex]\( f(a) \)[/tex]-intercept, we need to determine the value of [tex]\( f(a) \)[/tex] when [tex]\( a = 0 \)[/tex]. This is also known as the y-intercept if you think of the function in terms of [tex]\( y = mx + b \)[/tex] format.
- Substitute [tex]\( a = 0 \)[/tex] in the function:
[tex]\[
f(0) = 71 + 72 \times 0
\][/tex]
- Simplifying this gives us:
[tex]\[
f(0) = 71
\][/tex]
- Therefore, the [tex]\( f(a) \)[/tex]-intercept is 71.

Putting it all together:
- The average rate of change is 72.
- The [tex]\( f(a) \)[/tex]-intercept is 71.

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