Question

Use the facts and graph below to write the equation for g(x).FACTS:- this graph shows g(x)- it looks like the graph of the parent function f(x)=x^2 However:- it has been reflected (flipped) over the x-axis.- it has been shifted down 4 units.- it has been shifted left 1 unit.Step 1: Start with the equation f(x)=x^2. Write the equation for the graph of g(x) that has been reflected, or flipped, over the x-axis.Step 2: use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has also been shifted down 4 units.Step 3: use the equation you wrote in step 2. Write the equation for the graph of g(x) that has been shifted left 1 unit.

Answer 1

-f(x) reflects f(x) over the x-axis

f(x) - a translates f(x) a units down.

f(x + b) translates f(x) b units to the left

1) Given f(x) = x², then g(x) = -f(x) = -x² is the graph of g(x) that has been reflected over the x-axis.

2) Given the function: h(x) = -x², then g(x) = h(x) - 4 = -x² - 4 is the equation for the graph of g(x) that has also been shifted down 4 units.

3) Given the function: k(x) = -x² - 4, then g(x) = k(x + 1) = -(x+1)² - 4 is the equation for the graph of g(x) that has been shifted left 1 unit.