Vertical and Horizontal Translations (SB Activity 8)

Front

What is a vertical translation in a function?

Back

A vertical translation occurs when a function is shifted up or down on the graph. This is represented by adding or subtracting a constant to the function's output.

Front

How does the equation y = x^2 + 3 represent a vertical translation?

Back

This equation represents a vertical translation of the parent function y = x^2, shifted up 3 units.

Front

What is a horizontal translation in a function?

Back

A horizontal translation occurs when a function is shifted left or right on the graph. This is represented by adding or subtracting a constant to the function's input.

Front

How does the equation y = (x - 4)^2 represent a horizontal translation?

Back

This equation represents a horizontal translation of the parent function y = x^2, shifted right 4 units.

Front

What happens to the graph of f(x) = x^2 when we change it to g(x) = x^2 - 2?

Back

The graph of f(x) = x^2 shifts down 2 units to become g(x) = x^2 - 2.

Front

If f(x) = x^2, what is the equation for a graph that shifts up 5 units?

Back

The equation would be g(x) = x^2 + 5.

Front

What does the equation g(x) = 7(x + 3) represent in terms of translation?

Back

This equation represents a horizontal translation of the parent function f(x) = 7x, shifted left 3 units.

Front

How does the equation y = -x^2 + 4 differ from the parent function?

Back

This equation represents a vertical translation up 4 units and a reflection over the x-axis.

Front

What is the effect of the transformation w(x) = f(x + 2)?

Back

This transformation shifts the graph of f(x) left 2 units.

Front

If the function f(x) = x^2 is translated down 5 units, what is the new equation?

Back

The new equation is g(x) = x^2 - 5.