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

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

Given:

\[
f(x) = x^2 - x
\]

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

\[
g(x) = f(-x)
\]

Substitute \( -x \) into the function:

\[
g(x) = (-x)^2 - (-x)
\]

Simplify:

\[
g(x) = x^2 + x
\]

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

\[
g(x) = x^2 + x
\]

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 \( f(x) = x^2 - x \) when it is reflected over the origin?
3. Can you find the inverse of the function \( f(x) = x^2 - x \)?
4. How would you determine the vertex of the parabola described by \( g(x) = x^2 + x \)?
5. What is the axis of symmetry for the function \( g(x) = x^2 + x \)?

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

Understand how to reflect the quadratic function f(x) = x^2 - x over the y-axis to find g(x). Learn the step-by-step process of substituting -x into the function and simplifying the equation. Suitable for students studying reflections in quadratic functions in Grades 9-12.

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