MATH SOLVE

2 months ago

Q:
# The graph of the parent functionf(x) = x^2 is reflected across the y-axis. Write anequation for the function g after the reflection.Show your work. Based on your equation, whathappens to the graph? Explain.

Accepted Solution

A:

Answer:g(x) = x²The graph of g(x) is the same with the graph of f(x)Step-by-step explanation:* Lets explain how to solve the problem- If the function f(x) reflected across the x-axis, then the new function g(x) = - f(x)- If the function f(x) reflected across the y-axis, then the new function g(x) = f(-x)* Lets solve the problem∵ The parent function f(x) = x² is represent by upward parabola with vertex (0 , 0) (red graph in the attached picture)∵ f(x) is reflected across the y-axis- As the rule above reflection across the y-axis change the sign of x∴ g(x) = f(-x)∵ f(x) = x²∴ g(x) = (-x)²- Remember (-ve)^even number = (+ve)∴ (-x)² = x²∴ g(x) = x² - The function g(x) is represent by upward parabola with vertex (0 , 0) (black graph in the attached picture)∴ The graph of g(x) is the same with the graph of f(x)- The red graph and the black graph are coincide