Math Problem Statement

Find g(x), which is a reflection over the y-axis of f(x)=x^2-x

Solution

To find g(x)g(x), which is the reflection of the function f(x)=x2xf(x) = x^2 - x over the y-axis, you need to replace xx with x-x in the expression for f(x)f(x). This is because reflecting a function over the y-axis involves changing the sign of the xx-values.

Given:

f(x)=x2xf(x) = x^2 - x

The reflected function g(x)g(x) is:

g(x)=f(x)g(x) = f(-x)

Substitute x-x into the function:

g(x)=(x)2(x)g(x) = (-x)^2 - (-x)

Simplify:

g(x)=x2+xg(x) = x^2 + x

So, the function g(x)g(x) is:

g(x)=x2+xg(x) = x^2 + x

Would you like more details or have any questions?

Here are five related questions to explore further:

  1. How would you reflect a function over the x-axis instead of the y-axis?
  2. What happens to the graph of f(x)=x2xf(x) = x^2 - x when it is reflected over the origin?
  3. Can you find the inverse of the function f(x)=x2xf(x) = x^2 - x?
  4. How would you determine the vertex of the parabola described by g(x)=x2+xg(x) = x^2 + x?
  5. What is the axis of symmetry for the function g(x)=x2+xg(x) = x^2 + x?

Tip: Reflections are transformations that can be used to change the orientation of a graph without altering its shape.

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Math Problem Analysis

Mathematical Concepts

Reflections
Quadratic Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12