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Sagot :
Sure, let's solve the problem step-by-step and graph the function [tex]\( c(x) = 2x + 2.00 \)[/tex].
### Step-by-Step Solution
1. Understanding the Function:
- The function [tex]\( c(x) = 2x + 2.00 \)[/tex] represents the cost of a taxi ride.
- [tex]\( x \)[/tex] represents the number of minutes.
- [tex]\( 2x \)[/tex] is the variable cost based on the time of the ride.
- The constant term [tex]\( 2.00 \)[/tex] represents the base fare independent of time.
2. Identifying Key Points:
- To graph this linear function, we need to determine a few key points.
- The y-intercept ([tex]\(y\)[/tex]-intercept) occurs when [tex]\( x = 0 \)[/tex]:
[tex]\( c(0) = 2(0) + 2.00 = 2.00 \)[/tex].
So, one point is [tex]\( (0, 2.00) \)[/tex].
- Find another point for better accuracy, such as when [tex]\( x = 5 \)[/tex]:
[tex]\( c(5) = 2(5) + 2.00 = 10 + 2.00 = 12.00 \)[/tex].
So, another point is [tex]\( (5, 12.00) \)[/tex].
3. Graphing the Function:
- Plot the points [tex]\( (0, 2.00) \)[/tex] and [tex]\( (5, 12.00) \)[/tex] on the graph.
- Draw a line through these points, extending it as needed.
- Label the [tex]\( x \)[/tex]-axis as "Minutes ([tex]\( x \)[/tex])".
- Label the [tex]\( y \)[/tex]-axis as "Cost (\[tex]$ c(x))". - Add a title to the graph: "Graph of \( c(x) = 2x + 2.00 \)". 4. Interpreting the Graph: - The graph will be a straight line with a slope of 2, indicating that the cost increases by $[/tex]2.00 for each additional minute.
- The line will start from the y-intercept at [tex]\( (0, 2.00) \)[/tex] and rise rapidly as [tex]\( x \)[/tex] increases.
### Graph Coordinate Points
- [tex]\( (0, 2.00) \)[/tex]
- [tex]\( (5, 12.00) \)[/tex]
### Finding the slope and plotting:
- Slope ([tex]\( m \)[/tex]) = 2.
- The graph passes through [tex]\( (0, 2.00) \)[/tex].
Draw a straight line through these points to represent the linear relationship described by the function.
### Final Graph Features:
- The [tex]\( x \)[/tex]-axis (horizontal) should be labeled with minutes.
- The [tex]\( y \)[/tex]-axis (vertical) should be labeled with cost (in dollars).
- The graph line represents the function [tex]\( c(x) = 2x + 2.00 \)[/tex].
By following these instructions, you will clearly represent the cost of a taxi ride as a function of time on a graph paper. Ensure the labels and title are included for clarity.
### Step-by-Step Solution
1. Understanding the Function:
- The function [tex]\( c(x) = 2x + 2.00 \)[/tex] represents the cost of a taxi ride.
- [tex]\( x \)[/tex] represents the number of minutes.
- [tex]\( 2x \)[/tex] is the variable cost based on the time of the ride.
- The constant term [tex]\( 2.00 \)[/tex] represents the base fare independent of time.
2. Identifying Key Points:
- To graph this linear function, we need to determine a few key points.
- The y-intercept ([tex]\(y\)[/tex]-intercept) occurs when [tex]\( x = 0 \)[/tex]:
[tex]\( c(0) = 2(0) + 2.00 = 2.00 \)[/tex].
So, one point is [tex]\( (0, 2.00) \)[/tex].
- Find another point for better accuracy, such as when [tex]\( x = 5 \)[/tex]:
[tex]\( c(5) = 2(5) + 2.00 = 10 + 2.00 = 12.00 \)[/tex].
So, another point is [tex]\( (5, 12.00) \)[/tex].
3. Graphing the Function:
- Plot the points [tex]\( (0, 2.00) \)[/tex] and [tex]\( (5, 12.00) \)[/tex] on the graph.
- Draw a line through these points, extending it as needed.
- Label the [tex]\( x \)[/tex]-axis as "Minutes ([tex]\( x \)[/tex])".
- Label the [tex]\( y \)[/tex]-axis as "Cost (\[tex]$ c(x))". - Add a title to the graph: "Graph of \( c(x) = 2x + 2.00 \)". 4. Interpreting the Graph: - The graph will be a straight line with a slope of 2, indicating that the cost increases by $[/tex]2.00 for each additional minute.
- The line will start from the y-intercept at [tex]\( (0, 2.00) \)[/tex] and rise rapidly as [tex]\( x \)[/tex] increases.
### Graph Coordinate Points
- [tex]\( (0, 2.00) \)[/tex]
- [tex]\( (5, 12.00) \)[/tex]
### Finding the slope and plotting:
- Slope ([tex]\( m \)[/tex]) = 2.
- The graph passes through [tex]\( (0, 2.00) \)[/tex].
Draw a straight line through these points to represent the linear relationship described by the function.
### Final Graph Features:
- The [tex]\( x \)[/tex]-axis (horizontal) should be labeled with minutes.
- The [tex]\( y \)[/tex]-axis (vertical) should be labeled with cost (in dollars).
- The graph line represents the function [tex]\( c(x) = 2x + 2.00 \)[/tex].
By following these instructions, you will clearly represent the cost of a taxi ride as a function of time on a graph paper. Ensure the labels and title are included for clarity.
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