Question
The graph of f(x) = -2x squared is given below. Write the equation of a function g(x) which would shift the graph of f(x) right 2 units and down 6 units.
Answers
GPT 3.5
To shift the graph of f(x) right 2 units and down 6 units, we need to adjust the original equation f(x) = -2x^2 accordingly.
The general formula for shifting a function f(x) right a units and down b units is: g(x) = f(x - a) - b
In this case, a = 2 and b = 6. So the equation of the new function g(x) would be:
g(x) = -2(x - 2)^2 - 6
Therefore, the equation of the function g(x) which would shift the graph of f(x) right 2 units and down 6 units is g(x) = -2(x - 2)^2 - 6.
The general formula for shifting a function f(x) right a units and down b units is: g(x) = f(x - a) - b
In this case, a = 2 and b = 6. So the equation of the new function g(x) would be:
g(x) = -2(x - 2)^2 - 6
Therefore, the equation of the function g(x) which would shift the graph of f(x) right 2 units and down 6 units is g(x) = -2(x - 2)^2 - 6.