Math Problem Statement

Determine whether the function y = x^2 + x - 2 is linear or nonlinear. Explain your reasoning.

Solution

Let me analyze the uploaded image and provide an explanation for the problem.The problem asks to determine whether the function y=x2+x2y = x^2 + x - 2 is linear or nonlinear, and to explain the reasoning.

Solution:

A linear function is a function that can be written in the form: y=mx+b,y = mx + b, where mm and bb are constants, and the graph is a straight line. Linear functions have the following characteristics:

  • The highest power of xx is 1.
  • The function involves only xx-terms raised to the first power.

Now examining the given function: y=x2+x2.y = x^2 + x - 2.

  • The term x2x^2 involves a power of xx greater than 1, making this function nonlinear.
  • Graphically, this function represents a parabola, not a straight line, due to the quadratic term x2x^2.

Conclusion:

The function y=x2+x2y = x^2 + x - 2 is nonlinear because it includes the quadratic term x2x^2, and its graph is not a straight line.

Would you like more details about this problem or further clarifications?


Related Questions:

  1. What are the key differences between linear and quadratic functions?
  2. How can you graph y=x2+x2y = x^2 + x - 2 to verify its nonlinearity?
  3. What is the vertex form of a quadratic equation, and how does it relate to this function?
  4. Can a function with higher powers of xx (e.g., x3x^3) ever be linear? Why or why not?
  5. How does the coefficient of x2x^2 affect the shape of a quadratic function?

Tip:

Always check the degree of the polynomial in a function to quickly determine if it is linear, quadratic, or another type!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Quadratic Functions

Formulas

Linear function formula y = mx + b

Theorems

Definition of a linear function

Suitable Grade Level

Grades 8-10