https://file.aiquickdraw.com/mathbot/file/1728638267567v5ix93xj.jpg

Let's break down the tasks based on the image you provided, which consists of two exercises: 4.9 and 4.10.

### 4.9
This question refers to a graph of a function \( f \) with the domain \( D_f = [-1, 5] \).

#### a. **Finn nullpunktene til \( f \)**  
Find the zeros of the function \( f \) (the points where the graph intersects the x-axis).

- From the graph, the function crosses the x-axis at \( x = 0 \) and \( x = 4 \).
- Therefore, the **zeros of \( f \)** are \( x = 0 \) and \( x = 4 \).

#### b. **Hva er verdimengden til \( f \)?**  
Find the range of the function \( f \).

- From the graph, the minimum value of \( f(x) \) is \( -4 \) (at \( x \approx 3 \)) and the maximum value is \( 10 \) (at \( x = -1 \)).
- Thus, the **range of \( f \)** is \( [-4, 10] \).

#### c. **Finn \( f(0) \)**  
Find the value of \( f(0) \).

- Looking at the graph, when \( x = 0 \), \( f(x) = 4 \).
- Therefore, \( f(0) = 4 \).

#### d. **For hvilke verdier av \( x \) er \( f(x) = 4 \)?**  
Find the values of \( x \) for which \( f(x) = 4 \).

- From the graph, \( f(x) = 4 \) at \( x = 0 \) and \( x = 2 \).
- Therefore, the **values of \( x \) where \( f(x) = 4 \)** are \( x = 0 \) and \( x = 2 \).

### 4.10
The functions \( f(x) = x^2 - 4 \) and \( g(x) = 4 - x^2 \) are given.

#### a. **Finn eventuelle toppunkter og bunnpunkter på grafene**  
Find the possible maximum and minimum points on the graphs.

- For \( f(x) = x^2 - 4 \):
  - This is a parabola opening upwards. The vertex, which is the minimum point, is at \( x = 0 \), and \( f(0) = -4 \). Therefore, the minimum point is \( (0, -4) \).
  
- For \( g(x) = 4 - x^2 \):
  - This is a parabola opening downwards. The vertex, which is the maximum point, is at \( x = 0 \), and \( g(0) = 4 \). Therefore, the maximum point is \( (0, 4) \).

#### b. **Finn skjæringspunktene mellom grafene**  
Find the intersection points of the graphs.

- To find where \( f(x) = g(x) \), solve \( x^2 - 4 = 4 - x^2 \).
  \[
  2x^2 = 8 \quad \Rightarrow \quad x^2 = 4 \quad \Rightarrow \quad x = \pm 2
  \]
  - For \( x = 2 \), \( f(2) = g(2) = 0 \), and for \( x = -2 \), \( f(-2) = g(-2) = 0 \).
  - Therefore, the intersection points are \( (2, 0) \) and \( (-2, 0) \).

#### c. **Finn nullpunktene til funksjonene**  
Find the zeros of the functions.

- For \( f(x) = x^2 - 4 \), solve \( x^2 - 4 = 0 \). The solutions are \( x = \pm 2 \).
  - The zeros of \( f(x) \) are \( x = 2 \) and \( x = -2 \).

- For \( g(x) = 4 - x^2 \), solve \( 4 - x^2 = 0 \). The solutions are also \( x = \pm 2 \).
  - The zeros of \( g(x) \) are \( x = 2 \) and \( x = -2 \).

---

Do you need more details or clarifications on any of these points?  
Here are some additional questions that might expand on the above content:

1. What are the exact coordinates of the minimum and maximum points for other quadratic functions?
2. How can you verify the intersection points of two functions algebraically?
3. Can you explore the vertex form of a quadratic equation to analyze the function behavior?
4. What is the significance of the range of a function in real-world applications?
5. How do the zeros of a function relate to its graphical representation?

**Tip:** Remember that the zeros of a function are the points where the graph intersects the x-axis. These points give valuable information about the behavior of the function.

The user submitted an image containing two math problems, one related to finding the zeros, range, and specific values of a function, and the other involving intersections and zeros of quadratic functions.

This page provides step-by-step solutions to finding the zeros, range, and specific values for quadratic functions. Also covers how to find the intersection points of the quadratic functions f(x) = x^2 - 4 and g(x) = 4 - x^2. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation