Math Problem Statement

Determine based on the graph: i) The zeros of the function f ii) The value of the function when x = -2 iii) The values of x where the function f(x) = -2

Solution

Let's analyze the graph based on the three tasks:

i) Funktion f nollakohdat (Zero points of the function f):

The zero points are where the function f(x)=0f(x) = 0. This occurs where the curve intersects the x-axis. Based on the graph, the function has zero points at: x=3andx=1x = -3 \quad \text{and} \quad x = 1

ii) Funktion f arvo, kun x=2x = -2 (Value of the function when x=2x = -2):

At x=2x = -2, we can observe the y-coordinate on the graph, which is around 2. Therefore: f(2)=2f(-2) = 2

iii) Ne muuttujan arvot, joilla funktio f saa arvon -2 (The values of xx where the function f(x)=2f(x) = -2):

We need to find where the graph intersects the line y=2y = -2. Based on the graph, the function takes the value 2-2 at two points: x=1andx=0x = -1 \quad \text{and} \quad x = 0

Summary:

  1. Zero points: x=3x = -3 and x=1x = 1
  2. f(2)=2f(-2) = 2
  3. f(x)=2f(x) = -2 at x=1x = -1 and x=0x = 0

Would you like further details on any of these?

Here are 5 related questions to explore further:

  1. What is the maximum value of the function based on the graph?
  2. What is the minimum value of the function?
  3. What is the behavior of the function as xx \to \infty?
  4. Can you derive the equation of the function based on the graph?
  5. How would you interpret the slope at various points on this graph?

Tip:

When analyzing graphs, always look at where the function intersects key lines (such as the x-axis and y-axis) for important values like zeros and y-intercepts.

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Math Problem Analysis

Mathematical Concepts

Graph Interpretation
Zeros of a Function
Function Values

Formulas

f(x) = 0 for zeros
f(-2) for value of the function

Theorems

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Suitable Grade Level

Grades 9-10