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

To find: a) (fog)(5) b) (fog)(x) and its domain

Answered: Answer: Answer: 9. Let f(x) = 3x – 2…

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)

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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Concept explainers

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.

Question

100%

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

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