Math Problem Statement

Nedan visas grafen till funktion y = f(x). Använd grafen att: a) Beräkna f(2) b) Lösa ekvationen f(x) = 14

Solution

Let's analyze the graph and answer the questions based on it.

The graph shows the function y=f(x)y = f(x). You are asked to:

a) Beräkna f(2)f(2)
This asks you to find the value of the function f(x)f(x) at x=2x = 2. Look at the graph where x=2x = 2 and find the corresponding yy-value.

From the graph:

  • At x=2x = 2, the value of f(x)f(x) is y=4y = 4.

Thus, f(2)=4f(2) = 4.


b) Lösa ekvationen f(x)=14f(x) = 14
This asks for the values of xx where f(x)=14f(x) = 14. Look at the graph and find the xx-values where the yy-coordinate equals 14.

From the graph:

  • f(x)=14f(x) = 14 occurs at two points: x=12x = -12 and x=12x = 12.

Thus, the solutions to f(x)=14f(x) = 14 are x=12x = -12 and x=12x = 12.


Would you like further explanation or have any questions?

Here are five related questions you can explore:

  1. What is the value of f(10)f(-10)?
  2. What is the value of f(0)f(0)?
  3. Solve the equation f(x)=10f(x) = 10.
  4. At which xx-values does the graph have local maxima or minima?
  5. Determine the intervals where the function is increasing or decreasing.

Tip: Always ensure to carefully analyze the scale of both the x-axis and y-axis when reading off values from a graph.

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Math Problem Analysis

Mathematical Concepts

Graph Reading
Function Evaluation
Solving Equations

Formulas

Function Evaluation: f(x)
Equation Solving for f(x)

Theorems

Basic Graphing Theorems

Suitable Grade Level

Grades 8-10