Pregunta
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Sketch the graph of the function. \( f(x)=5 x+5 \)

Ask by Sanders Hall. in the United States
Mar 14,2025

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To sketch the graph of \( f(x) = 5x + 5 \), plot the y-intercept at \( (0, 5) \) and another point like \( (1, 10) \). Draw a straight line through these points to represent the function.

Solución

To sketch the graph of the function \( f(x) = 5x + 5 \), we can follow these steps: 1. **Identify the type of function**: This is a linear function, which means its graph will be a straight line. 2. **Determine the slope and y-intercept**: - The slope \( m \) is the coefficient of \( x \), which is \( 5 \). - The y-intercept \( b \) is the constant term, which is \( 5 \). This means the line crosses the y-axis at the point \( (0, 5) \). 3. **Find another point on the line**: - To find another point, we can choose a value for \( x \). Let's use \( x = 1 \): \[ f(1) = 5(1) + 5 = 10 \] - So, another point on the line is \( (1, 10) \). 4. **Plot the points**: - Plot the points \( (0, 5) \) and \( (1, 10) \) on a coordinate plane. 5. **Draw the line**: - Connect the points with a straight line, extending it in both directions. 6. **Label the axes**: - Make sure to label the x-axis and y-axis for clarity. The graph will be a straight line that rises steeply due to the slope of \( 5 \). The line will cross the y-axis at \( (0, 5) \) and will continue upward as \( x \) increases.

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The Deep Dive

To sketch the graph of the function \( f(x) = 5x + 5 \), start by identifying key points. The function is a linear equation with a slope of 5, which means the line will rise steeply as you move from left to right. The y-intercept, which is where the line crosses the y-axis, is at (0, 5). To plot it, begin at (0, 5) and then use the slope to find another point; from (0, 5), go up 5 units and right 1 unit to reach (1, 10). Connecting these points gives you a straight line that continues infinitely in both directions. The line can also be understood as representing a real-world scenario, such as budgeting. Imagine the function describes your spending, where \( x \) is the number of items purchased and \( f(x) \) is the total cost. If each item costs $5, the function tells you that even if you don't buy anything (at \( x = 0 \)), you'll still have a minimum expense of $5, which might be a base fee or initial cost. So, whether for budgeting or a graph, this linear function is quite practical!

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