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\begin{tabular}{l} Sketch a graph of \( f \) \\ \( f(x)=5-x \) \\ \hline\end{tabular}

Ask by Brewer Byrd. in the United States
Mar 13,2025

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To sketch the graph of \( f(x) = 5 - x \), plot the y-intercept at \( (0, 5) \) and draw a straight line with a slope of \(-1\) through this point. The line will pass through \( (1, 4) \) and continue descending from left to right.

Solución

To sketch the graph of the function \( f(x) = 5 - x \), we can follow these steps: 1. **Identify the type of function**: The function \( f(x) = 5 - x \) is a linear function. It can be rewritten in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. 2. **Determine the slope and y-intercept**: - The slope \( m \) is \(-1\) (the coefficient of \( x \)). - The y-intercept \( b \) is \( 5 \) (the constant term). 3. **Plot the y-intercept**: Start by plotting the point \( (0, 5) \) on the graph. 4. **Use the slope to find another point**: From the y-intercept, use the slope to find another point. Since the slope is \(-1\), this means that for every 1 unit you move to the right (positive direction on the x-axis), you move down 1 unit (negative direction on the y-axis). - From \( (0, 5) \), moving 1 unit to the right gives \( (1, 4) \). 5. **Draw the line**: Connect the points \( (0, 5) \) and \( (1, 4) \) with a straight line. Since this is a linear function, the line will continue infinitely 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 descends from left to right, crossing the y-axis at \( 5 \) and the x-axis at \( 5 \) (where \( f(x) = 0 \)). If you need a visual representation, you can use graphing software or tools to plot it accurately.

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Mind Expander

To graph the function \( f(x) = 5 - x \), you can start with the y-intercept, which occurs when \( x = 0 \). Plugging in 0 gives you \( f(0) = 5 \), so the graph crosses the y-axis at (0, 5). Next, determine another point by choosing a value for \( x \)—for instance, when \( x = 5 \), you find \( f(5) = 0 \), so the graph also passes through (5, 0). Now, plot these points and draw a straight line connecting them, extending in both directions, as this is a linear function. Voilà! You have your graph! Make sure to label the axes and points clearly for better clarity, and remember that the slope of the line is negative, indicating that as \( x \) increases, \( f(x) \) decreases. This creates a neat, downward sloping line from left to right!

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