**Instructional Content for Educational Website****Topic:** Solving Inequalities Using Graphs**Objective:** Given the graph of the function f(x), solve for the intervals where:1. $ f(x) > 0 $2. $ f(x) < 0 $### Graph Explanation:The provided graph illustrates a quadratic function which opens upwards, forming a parabola. The key features of this graph include:- **X-axis (horizontal axis):** Represents the variable $ x $.- **Y-axis (vertical axis):** Represents the function value $ f(x) $.- **Vertex:** The lowest point on the parabola occurs at approximately $ (6, -4) $.- **Intercepts:** The graph crosses the x-axis (where $ f(x) = 0 $) at approximately $ x = 5 $ and $ x = 7 $.### Problem Statement:Given the graph of $ f(x) $, solve the following:a) Find the intervals where $ f(x) > 0 $.b) Find the intervals where $ f(x) < 0 $.### Multiple Choice Questions:#### 1. Choose the correct solution for $ f(x) > 0 $:- **A.** $ 5 \leq x \leq 7 $- **B.** $ x < 5 $ or $ x > 7 $- **C.** $ 5 < x < 7 $- **D.** $ x \leq 5 $ or $ x \geq 7 $#### 2. Choose the correct solution for $ f(x) < 0 $:- **A.** $ x \leq 5 $ or $ x \geq 7 $- **B.** $ 5 < x < 7 $- **C.** $ x < 5 $ or $ x > 7 $- **D.** $ 5 \leq x \leq 7 $### Explanation:- **For $ f(x) > 0 $:** From the graph, we see that the function $ f(x) $ is above the x-axis (positive) to the left of $ x = 5 $ and to the right of $ x = 7 $. Therefore, the solution should capture these intervals

According to the given graph the function is: f(x) = (x - 6)2 - 1

Given the graph of f(x), solve a) f(x) > 0 and b) f(x) < 0. Choose the correct solution for f(x) > 0. O A. 5sxs7 O B. x < 5 or x > 7 O C. 5 < x < 7 O D. xs5 or x27 Choose the correct solution for f(x) < 0. O A. xs5 or x27 O B. 5 < x < 7 OC. x < 5 or x > 7 O D. 5sxs7

Given the graph of f(x), solve a) f(x) > 0 and b) f(x) < 0. Choose the correct solution for f(x) > 0. O A. 5sxs7 O B. x < 5 or x > 7 O C. 5 < x < 7 O D. xs5 or x27 Choose the correct solution for f(x) < 0. O A. xs5 or x27 O B. 5 < x < 7 OC. x < 5 or x > 7 O D. 5sxs7

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

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

**Instructional Content for Educational Website**

**Topic:** Solving Inequalities Using Graphs

**Objective:** Given the graph of the function f(x), solve for the intervals where:
1. $ f(x) > 0 $
2. $ f(x) < 0 $

### Graph Explanation:
The provided graph illustrates a quadratic function which opens upwards, forming a parabola. The key features of this graph include:

- **X-axis (horizontal axis):** Represents the variable $ x $.
- **Y-axis (vertical axis):** Represents the function value $ f(x) $.
- **Vertex:** The lowest point on the parabola occurs at approximately $ (6, -4) $.
- **Intercepts:** The graph crosses the x-axis (where $ f(x) = 0 $) at approximately $ x = 5 $ and $ x = 7 $.

### Problem Statement:
Given the graph of $ f(x) $, solve the following:
a) Find the intervals where $ f(x) > 0 $.
b) Find the intervals where $ f(x) < 0 $.

### Multiple Choice Questions:

#### 1. Choose the correct solution for $ f(x) > 0 $:
- **A.** $ 5 \leq x \leq 7 $
- **B.** $ x < 5 $ or $ x > 7 $
- **C.** $ 5 < x < 7 $
- **D.** $ x \leq 5 $ or $ x \geq 7 $

#### 2. Choose the correct solution for $ f(x) < 0 $:
- **A.** $ x \leq 5 $ or $ x \geq 7 $
- **B.** $ 5 < x < 7 $
- **C.** $ x < 5 $ or $ x > 7 $
- **D.** $ 5 \leq x \leq 7 $

### Explanation:

- **For $ f(x) > 0 $:**
From the graph, we see that the function $ f(x) $ is above the x-axis (positive) to the left of $ x = 5 $ and to the right of $ x = 7 $. Therefore, the solution should capture these intervals

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