Question

a consultant for a major computer company receives $2250 per month as a fee no matter how many hours he works. a. using x to represent the number of hours the consultant works each month, write a function, f, in symbolic form to represent the total amount received from the company each month. b. complete the table of values when the hours worked each month are 15, 25, and 35. c. use your graphing calculator to sketch the graph of this function. d. what is the slope of the line? what is the practical meaning of the slope in this situation? e. describe the graph of the function. a. the function is f(x)= . (use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Identify the nature of the function

The consultant's fee is a fixed - amount per month regardless of the number of hours worked. So it is a constant function.
$f(x)=2250$

Step2: Analyze the slope

For a constant function $y = c$ (where $c$ is a constant), the slope $m = 0$. In the context of this situation, the slope being 0 means that the amount of money the consultant receives does not change with the number of hours worked.

Step3: Describe the graph

The graph of the function $y = 2250$ is a horizontal line. The $y$ - intercept is 2250, and for every value of $x$ (number of hours worked), the $y$ - value (amount received) is always 2250.

Answer:

a. $f(x)=2250$
d. Slope of the line: $m = 0$. The practical meaning of the slope is that the amount of money the consultant receives does not depend on the number of hours worked.
e. The graph of the function is a horizontal line at $y = 2250$.