SOLUTION: Given the function f(x) = x^2 (x-squared). Find the function g(x) performing on f(x) a reflection in the X-axis followed by a downward shift of 6 units. Find the function h(

Algebra ->  Functions -> SOLUTION: Given the function f(x) = x^2 (x-squared). Find the function g(x) performing on f(x) a reflection in the X-axis followed by a downward shift of 6 units. Find the function h(      Log On


   

Question 1125077: Given the function f(x) = x^2 (x-squared).
Find the function g(x) performing on f(x) a reflection in the X-axis followed by a downward shift of 6 units.

Find the function h(x) performing on f(x) a horizontal shift of three units to the right followed by a reflection in the X-axis.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
equation is f(x) = x^2

reflection in the x-axis and a subsequent downward shift of 6 units gets you g(x) = -x^2 - 6

horizontal shift of 3 units to the right followed by a reflection in the x-axis gets you h(x) = -(x-3)^2

here's the graph of these functions.

the progression is from red to blue to green, with green being the final position of the graph.

first graph is first problem.

second graph is second problem.

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