Answer:
The new function g(x) will be ⇒ g(x) = f(-x)² - 7
Explanation:
* Lets take about the transformation
- 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)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) - k
* In the problem
- You will shift f(x) 7 units down and reflect it across the y-axis
- That means we will subtract f(x) by 7 and change x to -x
* The new function g(x) will be
g(x) = f(-x) - 7
* Look to the graph
- The red graph is f(x) = x²
- The blue graph is g(x) = (-x)² - 7