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Use transformations of f(x) = x° to graph the following function. g(x) = - 4(x + 4)? - 3 Select all the transformations that are needed to graph the given function using f(x) =x?. | A. Reflect the graph about the x-axis. B. Stretch the graph horizontally by a factor of 3. O C. Reflect the graph about the y-axis. | D. Stretch the graph vertically by a factor of 4. | E. Shift the graph 4 units to the left. |F. Shift the graph 3 units down. | G. Shrink the graph vertically by a factor of 4. H. Shift the graph 3 units up. I. Shrink the graph horizontally by a factor of 3. O J. Shift the graph 4 units to the right.

Use transformations of f(x) = x° to graph the following function. g(x) = - 4(x + 4)? - 3 Select all the transformations that are needed to graph the given function using f(x) =x?. | A. Reflect the graph about the x-axis. B. Stretch the graph horizontally by a factor of 3. O C. Reflect the graph about the y-axis. | D. Stretch the graph vertically by a factor of 4. | E. Shift the graph 4 units to the left. |F. Shift the graph 3 units down. | G. Shrink the graph vertically by a factor of 4. H. Shift the graph 3 units up. I. Shrink the graph horizontally by a factor of 3. O J. Shift the graph 4 units to the right.

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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**Transformations of Quadratic Functions** To graph the function \( g(x) = -4(x + 4)^2 - 3 \) using transformations of \( f(x) = x^2 \), select all necessary transformations from the list provided. ### Transformation Options: - **A.** Reflect the graph about the x-axis. - **B.** Stretch the graph horizontally by a factor of 3. - **C.** Reflect the graph about the y-axis. - **D.** Stretch the graph vertically by a factor of 4. - **E.** Shift the graph 4 units to the left. - **F.** Shift the graph 3 units down. - **G.** Shrink the graph vertically by a factor of 4. - **H.** Shift the graph 3 units up. - **I.** Shrink the graph horizontally by a factor of 3. - **J.** Shift the graph 4 units to the right. ### Explanation of Transformations: 1. **Vertical Reflection:** A reflection over the x-axis changes \( f(x) \) to \( -f(x) \), indicated by the negative sign outside the function. 2. **Horizontal Shift:** Shifting \( x \) to the left or right is achieved by adding or subtracting from the \( x \)-value inside the function. 3. **Vertical Stretch:** Multiplying the entire function by a factor stretches or compresses the graph vertically. 4. **Vertical Shift:** A vertical shift up or down is represented by adding or subtracting a constant outside the function. Choose the transformations that match the equation \( g(x) = -4(x + 4)^2 - 3 \).
Transcribed Image Text:**Transformations of Quadratic Functions** To graph the function \( g(x) = -4(x + 4)^2 - 3 \) using transformations of \( f(x) = x^2 \), select all necessary transformations from the list provided. ### Transformation Options: - **A.** Reflect the graph about the x-axis. - **B.** Stretch the graph horizontally by a factor of 3. - **C.** Reflect the graph about the y-axis. - **D.** Stretch the graph vertically by a factor of 4. - **E.** Shift the graph 4 units to the left. - **F.** Shift the graph 3 units down. - **G.** Shrink the graph vertically by a factor of 4. - **H.** Shift the graph 3 units up. - **I.** Shrink the graph horizontally by a factor of 3. - **J.** Shift the graph 4 units to the right. ### Explanation of Transformations: 1. **Vertical Reflection:** A reflection over the x-axis changes \( f(x) \) to \( -f(x) \), indicated by the negative sign outside the function. 2. **Horizontal Shift:** Shifting \( x \) to the left or right is achieved by adding or subtracting from the \( x \)-value inside the function. 3. **Vertical Stretch:** Multiplying the entire function by a factor stretches or compresses the graph vertically. 4. **Vertical Shift:** A vertical shift up or down is represented by adding or subtracting a constant outside the function. Choose the transformations that match the equation \( g(x) = -4(x + 4)^2 - 3 \).
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