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1 Describe how g(x) = f(x) transforms the graph of the parent function ƒ(x). -3 Ņ The graph is narrower. The graph is wider. The graph is reflected. T 5 4 3 2 - -2 3 41-axis The graph has moved 5 units down. 2 f(x) ♡ x-axis

1 Describe how g(x) = f(x) transforms the graph of the parent function ƒ(x). -3 Ņ The graph is narrower. The graph is wider. The graph is reflected. T 5 4 3 2 - -2 3 41-axis The graph has moved 5 units down. 2 f(x) ♡ x-axis

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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**Understanding Graph Transformations** **Problem Statement:** Describe how \( g(x) = \frac{1}{5} f(x) \) transforms the graph of the parent function \( f(x) \). **Visual Aid:** The image includes a graph of the function \( f(x) \). The graph is a parabola opening upwards with its vertex at the origin (0,0). The x-axis ranges from -4 to 4, and the y-axis ranges from -3 to 5. **Explanation of the Graph:** - The parabola \( f(x) \) is symmetric with respect to the y-axis. - It intersects the x-axis at \( x = -2 \) and \( x = 2 \). - The graph has been drawn on a coordinate plane with grid lines for clarity. **Multiple Choice Options:** 1. The graph is narrower. 2. The graph is wider. 3. The graph is reflected. 4. The graph has moved 5 units down. **Analysis:** Applying the transformation \( g(x) = \frac{1}{5} f(x) \): - The transformation describes a vertical compression. - This causes the graph to widen because multipliers between 0 and 1 compress the graph vertically. **Correct Choice:** - The graph is wider. **Conclusion:** Through this transformation, \( g(x) = \frac{1}{5} f(x) \), the graph of the parent function \( f(x) \) becomes wider. This transformation vertically compresses the graph by a factor of \( \frac{1}{5} \), making it appear stretched along the y-axis.
Transcribed Image Text:**Understanding Graph Transformations** **Problem Statement:** Describe how \( g(x) = \frac{1}{5} f(x) \) transforms the graph of the parent function \( f(x) \). **Visual Aid:** The image includes a graph of the function \( f(x) \). The graph is a parabola opening upwards with its vertex at the origin (0,0). The x-axis ranges from -4 to 4, and the y-axis ranges from -3 to 5. **Explanation of the Graph:** - The parabola \( f(x) \) is symmetric with respect to the y-axis. - It intersects the x-axis at \( x = -2 \) and \( x = 2 \). - The graph has been drawn on a coordinate plane with grid lines for clarity. **Multiple Choice Options:** 1. The graph is narrower. 2. The graph is wider. 3. The graph is reflected. 4. The graph has moved 5 units down. **Analysis:** Applying the transformation \( g(x) = \frac{1}{5} f(x) \): - The transformation describes a vertical compression. - This causes the graph to widen because multipliers between 0 and 1 compress the graph vertically. **Correct Choice:** - The graph is wider. **Conclusion:** Through this transformation, \( g(x) = \frac{1}{5} f(x) \), the graph of the parent function \( f(x) \) becomes wider. This transformation vertically compresses the graph by a factor of \( \frac{1}{5} \), making it appear stretched along the y-axis.
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