Transformations: Vertical and Horizontal Translation Review

Front

What is a vertical translation in the context of function transformations?

Back

A vertical translation involves shifting a function up or down on the graph without changing its shape.

Front

What is a horizontal translation in the context of function transformations?

Back

A horizontal translation involves shifting a function left or right on the graph without changing its shape.

Front

How do you represent a function that has been shifted to the right by 'h' units?

Back

g(x) = f(x - h), where h > 0.

Front

How do you represent a function that has been shifted to the left by 'h' units?

Back

g(x) = f(x + h), where h > 0.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x^2.

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is f(x) = |x|.

Front

If f(x) = |x|, what is the equation of the function shifted left 4 units and up 7 units?

Back

y = |x + 4| + 7.

Front

What effect does adding a constant 'k' to a function f(x) have?

Back

Adding a constant 'k' shifts the function vertically; if k > 0, it shifts up, and if k < 0, it shifts down.

Front

What effect does subtracting a constant 'h' from the input of a function f(x) have?

Back

Subtracting a constant 'h' shifts the function horizontally; if h > 0, it shifts right, and if h < 0, it shifts left.

Front

What is the general form of a vertically translated function?

Back

g(x) = f(x) + k, where k is the vertical shift.