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Answer: Answer: 9. Let f(x) = 3x – 2 and g(x) =-x+ 4. Find (fo g)(5). Answer: 10. Let f(x) = 3x+ 4 and g(x) = x². Find (fo g)(x) and its domain.

Answer: Answer: 9. Let f(x) = 3x – 2 and g(x) =-x+ 4. Find (fo g)(5). Answer: 10. Let f(x) = 3x+ 4 and g(x) = x². Find (fo g)(x) and its domain.

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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please answer 9 and 10! thank you

## Mathematics Practice Problems ### 5. Determine the equation of the graph below. Choose the correct equation. The given graph is a parabola opening upwards. Use the options below to determine the correct equation. a) \( y = (x - 2)^2 + 3 \) b) \( y = (x - 2)^2 - 3 \) c) \( y = (x + 2)^2 + 3 \) d) \( y = (x + 2)^2 - 3 \) **Graph:** - The vertex of the parabola appears to be at \((-2, -3)\). ![Graph](image-link-here) ### 6. Graph \( f(x) = \sqrt{x + 2} - 3 \) **Graph:** - This is the plot of a transformed square root function. ![Graph](image-link-here) ### 7. & 8. Use the following functions for #7, 8. Let \( f(x) = 2x^2 + 3x \) and \( g(x) = x^2 + 4x \). 7. Find \( (f \circ g)(5) \) **Answer:** ______________________ 8. Find \( (f \circ g)(2) \) **Answer:** ______________________ ### 9. Let \( f(x) = 3x - 2 \) and \( g(x) = -x + 4 \). Find \( (f \circ g)(5) \). **Answer:** ______________________ ### 10. Let \( f(x) = 3x + 4 \) and \( g(x) = x^2 \). Find \( (f \circ g)(x) \) and its domain. **Answer:** _____________________________________________________ --- **Graph Explanations:** - **Graph in #5:** The graph provided is a parabola. By observing the vertex and comparing the given options, you should identify the correct parabola equation. - **Graph in #6:** The function \( f(x) = \sqrt{x + 2} - 3 \) is a square root function translated. The graph should shift left by 2 units and down by 3 units. Ensure to solve each problem step by step, plugging in values as needed, and making sure you understand the transformations of functions when graphing
Transcribed Image Text:## Mathematics Practice Problems ### 5. Determine the equation of the graph below. Choose the correct equation. The given graph is a parabola opening upwards. Use the options below to determine the correct equation. a) \( y = (x - 2)^2 + 3 \) b) \( y = (x - 2)^2 - 3 \) c) \( y = (x + 2)^2 + 3 \) d) \( y = (x + 2)^2 - 3 \) **Graph:** - The vertex of the parabola appears to be at \((-2, -3)\). ![Graph](image-link-here) ### 6. Graph \( f(x) = \sqrt{x + 2} - 3 \) **Graph:** - This is the plot of a transformed square root function. ![Graph](image-link-here) ### 7. & 8. Use the following functions for #7, 8. Let \( f(x) = 2x^2 + 3x \) and \( g(x) = x^2 + 4x \). 7. Find \( (f \circ g)(5) \) **Answer:** ______________________ 8. Find \( (f \circ g)(2) \) **Answer:** ______________________ ### 9. Let \( f(x) = 3x - 2 \) and \( g(x) = -x + 4 \). Find \( (f \circ g)(5) \). **Answer:** ______________________ ### 10. Let \( f(x) = 3x + 4 \) and \( g(x) = x^2 \). Find \( (f \circ g)(x) \) and its domain. **Answer:** _____________________________________________________ --- **Graph Explanations:** - **Graph in #5:** The graph provided is a parabola. By observing the vertex and comparing the given options, you should identify the correct parabola equation. - **Graph in #6:** The function \( f(x) = \sqrt{x + 2} - 3 \) is a square root function translated. The graph should shift left by 2 units and down by 3 units. Ensure to solve each problem step by step, plugging in values as needed, and making sure you understand the transformations of functions when graphing
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