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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8f54919-3719-4a11-8884-2432a8f20fd9%2F8a3b206c-1fbe-4e47-8867-2718dcd63dde%2Fcle5ev.jpeg&w=3840&q=75)
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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