Horizontal & Vertical Shifts of Linear Functions

Front

What is a horizontal shift in a linear function?

Back

A horizontal shift occurs when the input of the function is adjusted, resulting in the graph moving left or right on the coordinate plane.

Front

What is a vertical shift in a linear function?

Back

A vertical shift occurs when a constant is added or subtracted from the function's output, resulting in the graph moving up or down on the coordinate plane.

Front

Describe the transformation of f(x) that results in g(x): g(x) = f(x) - 2.

Back

f(x) has been translated down 2.

Front

Describe the transformation of f(x) that results in g(x): g(x) = f(x + 2) - 3.

Back

f(x) has been translated to the left 2 and down 3.

Front

Given f(x) = x - 3, translate the function down 5 and write the new rule.

Back

g(x) = x - 8.

Front

What is the parent function of a linear equation?

Back

The parent function of a linear equation is f(x) = x, which represents a straight line through the origin.

Front

How does adding a positive constant to a function affect its graph?

Back

Adding a positive constant shifts the graph of the function upward.

Front

How does subtracting a positive constant from a function affect its graph?

Back

Subtracting a positive constant shifts the graph of the function downward.

Front

What is the effect of g(x) = f(x - 4)?

Back

The graph of f(x) is translated to the right by 4 units.

Front

What is the effect of g(x) = f(x + 3)?

Back

The graph of f(x) is translated to the left by 3 units.