To graph the cost function [tex]\( c(x) = 2x + 2.00 \)[/tex], follow these steps:
1. Understand the Function:
The cost function [tex]\( c(x) = 2x + 2.00 \)[/tex] is a linear function where:
- The slope (rate of change) is 2, meaning the cost increases by [tex]$2 for every additional minute.
- The y-intercept is $[/tex]2.00, meaning if the number of minutes ([tex]\( x \)[/tex]) is 0, the initial cost is [tex]$2.00.
2. Create a Table of Values:
To plot points on the graph, choose a few values for \( x \) (minutes) and calculate the corresponding \( c(x) \) (cost):
\[
\begin{array}{c|c}
x & c(x) \\
\hline
0 & 2\cdot 0 + 2.00 = 2.00 \\
1 & 2\cdot 1 + 2.00 = 4.00 \\
2 & 2\cdot 2 + 2.00 = 6.00 \\
3 & 2\cdot 3 + 2.00 = 8.00 \\
\end{array}
\]
3. Plot the Points:
Plot these points on graph paper or a coordinate plane:
- (0, 2.00)
- (1, 4.00)
- (2, 6.00)
- (3, 8.00)
4. Draw the Line:
Since \( c(x) = 2x + 2.00 \) is a linear function, you can draw a straight line through these points.
5. Label Axes:
- The horizontal axis (x-axis) represents the number of minutes (\( x \)).
- The vertical axis (y-axis) represents the total cost in dollars (\( c(x) \)).
6. Check the Slope and Intercept:
- The y-intercept is at $[/tex]2.00. This point confirms the initial cost when [tex]\( x = 0 \)[/tex].
- The slope is 2, indicating the line should rise 2 units vertically for each 1 unit it moves horizontally.
Summary:
- Correct graph would show a straight line starting from the y-intercept at (0, 2.00).
- The line should have a slope of 2, meaning for each additional minute, the cost increases by [tex]$2.
- The x-axis should be labeled "Number of Minutes (\( x \))".
- The y-axis should be labeled "Cost ($[/tex]c(x)$)".
