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Which graph best represent the function f. (5, if x ≥1 f(x) = (-3-x, ifx<1 of 11 E

Which graph best represent the function f. (5, if x ≥1 f(x) = (-3-x, ifx<1 of 11 E

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcription for Educational Website: **Title: Understanding Piecewise Functions through Graphing** **Content:** This exercise asks, "Which graph best represents the function \( f \)?" The piecewise function \( f(x) \) is defined as follows: - \( f(x) = 5 \), if \( x \geq 1 \) - \( f(x) = -3 - x \), if \( x < 1 \) **Graph Explanation:** The provided coordinate system ranges from -6 to 6 on both the x-axis and y-axis, with the x-axis and y-axis crossing at the origin \((0,0)\). - **For \( x \geq 1 \):** The function is constant at \( y = 5 \). This implies a horizontal line on the graph starting from \((1, 5)\) and extending to the right indefinitely. - **For \( x < 1 \):** The function follows the linear equation \( y = -3 - x \), which is a straight line with a slope of -1 and a y-intercept at -3. The line should be plotted for values less than 1. When graphing piecewise functions, ensure that: - The transition at \( x = 1 \) is clearly depicted. Here, a filled or open circle is used at \( x = 1 \) to indicate whether that point is included in the segment. Since \( f(x) = 5 \) when \( x \geq 1 \), there will be a filled circle at point \((1, 5)\). - The linear portion \( y = -3 - x \) is graphed only for \( x < 1 \). Using this analysis, identify which graph correctly reflects these segments and transition points as per the function's conditions.
Transcribed Image Text:Transcription for Educational Website: **Title: Understanding Piecewise Functions through Graphing** **Content:** This exercise asks, "Which graph best represents the function \( f \)?" The piecewise function \( f(x) \) is defined as follows: - \( f(x) = 5 \), if \( x \geq 1 \) - \( f(x) = -3 - x \), if \( x < 1 \) **Graph Explanation:** The provided coordinate system ranges from -6 to 6 on both the x-axis and y-axis, with the x-axis and y-axis crossing at the origin \((0,0)\). - **For \( x \geq 1 \):** The function is constant at \( y = 5 \). This implies a horizontal line on the graph starting from \((1, 5)\) and extending to the right indefinitely. - **For \( x < 1 \):** The function follows the linear equation \( y = -3 - x \), which is a straight line with a slope of -1 and a y-intercept at -3. The line should be plotted for values less than 1. When graphing piecewise functions, ensure that: - The transition at \( x = 1 \) is clearly depicted. Here, a filled or open circle is used at \( x = 1 \) to indicate whether that point is included in the segment. Since \( f(x) = 5 \) when \( x \geq 1 \), there will be a filled circle at point \((1, 5)\). - The linear portion \( y = -3 - x \) is graphed only for \( x < 1 \). Using this analysis, identify which graph correctly reflects these segments and transition points as per the function's conditions.
**Which graph best represents the function f.** The function \( f(x) \) is defined as: \[ f(x) = \begin{cases} x + 5 & \text{if } x > 0 \\ 2 & \text{if } x \leq 0 \end{cases} \] **Graph Description:** - The graph is displayed on a coordinate plane with the x-axis and y-axis marked from -6 to 6. - For \( x > 0 \), the function is represented by the line \( y = x + 5 \), starting just after the y-intercept at \( y = 5 \). - For \( x \leq 0 \), the function is a horizontal line represented by \( y = 2 \). This line intersects the y-axis at \( y = 2 \) and extends leftward indefinitely. - The transition between the two pieces of the function occurs at \( x = 0 \). The graph shows an open circle at \( (0, 5) \) and a closed circle at \( (0, 2) \) to indicate the continuity of the second piece and the exclusion of the first.
Transcribed Image Text:**Which graph best represents the function f.** The function \( f(x) \) is defined as: \[ f(x) = \begin{cases} x + 5 & \text{if } x > 0 \\ 2 & \text{if } x \leq 0 \end{cases} \] **Graph Description:** - The graph is displayed on a coordinate plane with the x-axis and y-axis marked from -6 to 6. - For \( x > 0 \), the function is represented by the line \( y = x + 5 \), starting just after the y-intercept at \( y = 5 \). - For \( x \leq 0 \), the function is a horizontal line represented by \( y = 2 \). This line intersects the y-axis at \( y = 2 \) and extends leftward indefinitely. - The transition between the two pieces of the function occurs at \( x = 0 \). The graph shows an open circle at \( (0, 5) \) and a closed circle at \( (0, 2) \) to indicate the continuity of the second piece and the exclusion of the first.
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