Answer:
g(x) = x²
The 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
