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10x2 Given the function : y = f(x) = 1+x2 (a) Use the input values :

10x2 Given the function : y = f(x) = 1+x2 (a) Use the input values :

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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### Function Analysis Task 1. **Given the function: \( y = f(x) = \frac{10x^2}{1 + x^2} \)** (a) **Use the input values:** \( x = 0, \pm 1, \pm 2, \pm 3, \pm 7 \) to complete the table and sketch the graph. | \( x \) | \( y \) | |------- |--------| | 0 | | | 1 | | | -1 | | | 2 | | | -2 | | | 3 | | | -3 | | | 7 | | | -7 | | **Explanation of the graph:** The graph contains a Cartesian coordinate system with a grid. The X-axis and Y-axis are drawn as thick lines originating from the center and extending outward. You're expected to plot the values from the table onto this graph. (b) **Use your graph in part (a) to determine the domain and range of the function.** (c) **Identify the type of symmetry the function has.** (d) **Write on your graph where the function increases/decreases.** (e) **Use your graph to identify the horizontal asymptote/end behavior of the function.** ### Instructions for Students: 1. **Completing the Table:** - Calculate \( y \) for each given \( x \) by substituting \( x \) into the function \( y = \frac{10x^2}{1 + x^2} \). - Fill in the table based on your calculations. 2. **Graphing the Function:** - Plot each \((x, y)\) pair from the table onto the provided graph. - Draw the curve that represents the function based on these points. 3. **Analyzing the Graph:** - From the graph, determine the domain (all possible \( x \)-values) and range (all possible \( y \)-values) of the function. - Identify symmetry by observing if the graph is mirrored across any axis or point (e.g., symmetric around \( y \)-axis for even functions). - Note where the function is increasing (
Transcribed Image Text:### Function Analysis Task 1. **Given the function: \( y = f(x) = \frac{10x^2}{1 + x^2} \)** (a) **Use the input values:** \( x = 0, \pm 1, \pm 2, \pm 3, \pm 7 \) to complete the table and sketch the graph. | \( x \) | \( y \) | |------- |--------| | 0 | | | 1 | | | -1 | | | 2 | | | -2 | | | 3 | | | -3 | | | 7 | | | -7 | | **Explanation of the graph:** The graph contains a Cartesian coordinate system with a grid. The X-axis and Y-axis are drawn as thick lines originating from the center and extending outward. You're expected to plot the values from the table onto this graph. (b) **Use your graph in part (a) to determine the domain and range of the function.** (c) **Identify the type of symmetry the function has.** (d) **Write on your graph where the function increases/decreases.** (e) **Use your graph to identify the horizontal asymptote/end behavior of the function.** ### Instructions for Students: 1. **Completing the Table:** - Calculate \( y \) for each given \( x \) by substituting \( x \) into the function \( y = \frac{10x^2}{1 + x^2} \). - Fill in the table based on your calculations. 2. **Graphing the Function:** - Plot each \((x, y)\) pair from the table onto the provided graph. - Draw the curve that represents the function based on these points. 3. **Analyzing the Graph:** - From the graph, determine the domain (all possible \( x \)-values) and range (all possible \( y \)-values) of the function. - Identify symmetry by observing if the graph is mirrored across any axis or point (e.g., symmetric around \( y \)-axis for even functions). - Note where the function is increasing (
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