Write an equation that shows a vertical shift of 7 units up.

Question

Write the equation of an absolute value function shifted left 9.

Answer 1

The parent function for absolute value is:

y=|x|

To shift this 7 units up change to the following. + is the sign to move up. Vertical shift is outside the grouping symbol.

y=|x|+7

To shift this left 9 units it would change to the following: + is the sign to move to the left. Horizontal shift is inside the grouping symbol.

y=|x+9|

Answer 2

Let f(x) be your original function. Pick a function, any function. Then a vertical shift of +7 of that function would just be f(x) + 7.

Ex: f(x) = 3x² - 4

Then our shifted function, let's name it g(x)

g(x) = f(x) + 7

rewritten would be

g(x) = (3x² - 4) + 7 or g(x) = 3x² + 3.

For a horizontal shift, let's call it h(x)

h(x) = f(x - shift)

Using our example f(x) above with the requested shift of -9 (9 to the left, left is the negative direction):

h(x) = f(x - (-9)) = f(x+9) (just replace all x's in f(x) with x+9)

h(x) = 3(x+9)² - 4