https://file.aiquickdraw.com/mathbot/file/17266821059749ig1pcgg.jpg

Let's go through the graph and answer each of the questions step-by-step based on the visual information from the graph of \( f(x) \):

**a. Is the graph a function?**

- **Yes**, the graph represents a function. This is because it passes the *vertical line test*, meaning that any vertical line drawn through the graph intersects the curve at most once. This indicates that for every \( x \)-value, there is only one corresponding \( y \)-value.

**b. Evaluate the function for \( f(0) \)**

- To evaluate \( f(0) \), we locate \( x = 0 \) on the graph and find the corresponding \( y \)-value. From the graph, \( f(0) = 0 \).

**c. For what intervals is the function increasing?**

- The function is increasing where the graph moves upwards as \( x \) increases. Based on the graph:
  - The function is increasing on the intervals \( (-2, -1) \) and \( (0, 2) \).

**d. For what intervals is the function decreasing?**

- The function is decreasing where the graph moves downwards as \( x \) increases. From the graph:
  - The function is decreasing on the intervals \( (-\infty, -2) \), \( (-1, 0) \), and \( (2, \infty) \).

**e. What is the domain?**

- The domain of the function is the set of all \( x \)-values for which the function is defined. Since the graph extends indefinitely to the left and right, the domain is:
  - \( (-\infty, \infty) \).

**f. What is the range?**

- The range of the function is the set of all possible \( y \)-values that the graph reaches. From the graph, the lowest \( y \)-value is \(-1\), and the highest is 3. Therefore, the range is:
  - \( [-1, 3] \).

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What does the vertical line test confirm about functions?
2. How can you determine where a function is increasing or decreasing algebraically?
3. What is the significance of the domain and range in real-world applications of functions?
4. Can a function have more than one interval where it increases or decreases?
5. How does the concept of a function’s inverse relate to its graph?

**Tip:** When analyzing graphs, always check for key features like intercepts, intervals of increase/decrease, and extrema (maximum or minimum points) to fully understand the function's behavior.

Use the graph of f(x) to answer the following questions:
a. Is the graph a function?
b. Evaluate the function for f(0)
c. For what intervals is the function increasing?
d. For what intervals is the function decreasing?
e. What is the domain?
f. What is the range?

Explore how to analyze a function graph by answering questions on domain, range, and intervals of increase and decrease. Learn to evaluate f(0), apply the vertical line test, and identify key features of the function. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation