Function Transformations

x²-1

What is g(x)?

It is the graph of y = x² translated 2 units up and 5 units to the left.

A transformation of the graph of y = x² . Which statement correctly describes the graph of y = (x + 5)² + 2 ?

It is the graph of y = x² vertically stretched, and then translated 8 units up and 5 units to the left.

A transformation of the graph of y = x². Which statement correctly describes the graph of the equation shown below? y = 2(x + 5)² + 8

It is the graph of y = x² vertically compressed, and then translated 8 units down and 4 units to the left.

A transformation of the graph of y = x². Which statement correctly describes the graph of the equation shown below? y = 1/5 (x+4)² - 8

It is the graph of y = x² is translated 9 units up and 3 units to the right.

A transformation of the graph of y = x². Which statement correctly describes the graph of y = (x - 3)² + 9 ?

(x + 2)²

What is g(x)?

The graph of g(x) is the graph of f(x) shifted to the right 3 units.

Consider the function f(x) = x² and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)? g(x) = f(x - 3) = (x - 3)²

g(x) = x² - 6

If the graph of f(x) = x² is shifted down 6 units, then what would be the equation of the new graph?

The graph shifts right 2 units.

What happens to the graph of y = |x| when the equation changes to y = |x - 2|?

The graph shifts up 8 units.

What happens to the graph of y = |x| when the equation changes to y = |x| + 8?

The graph shifts up 9 units.

What happens to the graph of y = |x| when the equation changes to y = |x| + 9?

The graph shifts down 1 unit.

What happens to the graph of y = |x| when the equation changes to y = |x| - 1?

|x|−3

What is g(x)

It is the graph of y = |x| translated 2 units down and 9 units to the left.

A transformation of the graph of y = |x|. Which statement correctly describes the graph of y = |x + 9| - 2?

The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5.

Consider the function f(x) = x² and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)? g(x) = 5·f(x) = 5x²

Up

In which direction must the graph of f(x) = x² be shifted to produce the graph of g(x) = x² + 7?

Down

In which direction must the graph of f(x) = x² be shifted to produce the graph of g(x) = x² - 3?

The graph shifts 2 units up.

What happens to the graph of f(x) = |x| be shifted to produce the graph of g(x) = |x| + 2?