Math Problem Statement

Figuren viser 3 grafer, hvor en af dem er grafen for en lineær funktion y = ax + b. Hvilken graf er grafen for en lineær funktion?

Solution

The question is asking which of the three graphs in the image represents a linear function, which follows the form y=ax+by = ax + b.

Looking at the graph:

  • The yellow graph is a straight line, which is characteristic of a linear function because it has the form y=ax+by = ax + b (a straight line).
  • The orange graph and the blue graph are curved, meaning they cannot represent linear functions. They likely represent higher-degree polynomial functions or other non-linear types.

So, the yellow graph is the graph of a linear function.

Would you like further details or have any other questions?

Here are some related questions:

  1. How can you recognize a linear function from its equation?
  2. What are the characteristics of a polynomial graph?
  3. What are the effects of changing the slope aa and intercept bb in the equation y=ax+by = ax + b?
  4. Can a quadratic or cubic function ever appear as a straight line?
  5. How do you determine the degree of a polynomial function from its graph?

Tip: Linear functions always produce straight lines, whereas non-linear functions (like quadratics or cubics) result in curves.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Graphs of Functions
Polynomials

Formulas

y = ax + b

Theorems

Properties of Linear Functions

Suitable Grade Level

Grades 7-9