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Sagot :
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 ($[/tex]c(x)$)".
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 ($[/tex]c(x)$)".
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