Transformations in Function Notation

Front

What is a vertical translation in function notation?

Back

A vertical translation occurs when a constant is added to or subtracted from a function, shifting the graph up or down without changing its shape.

Front

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

Back

Adding a positive constant to a function results in a vertical translation of the graph upwards by that constant's value.

Front

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

Back

Subtracting a constant from a function results in a vertical translation of the graph downwards by that constant's value.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph, effectively flipping it upside down.

Front

What is the effect of multiplying a function by -1?

Back

Multiplying a function by -1 reflects the graph over the x-axis.

Front

What is a horizontal stretch in function notation?

Back

A horizontal stretch occurs when the input variable x is multiplied by a fraction, causing the graph to stretch away from the y-axis.

Front

How does the expression g(x) = f(kx) affect the graph of f(x) when k > 1?

Back

When k > 1, the graph of f(x) is compressed horizontally, making it narrower.

Front

How does the expression g(x) = f(kx) affect the graph of f(x) when 0 < k < 1?

Back

When 0 < k < 1, the graph of f(x) is stretched horizontally, making it wider.

Front

What is the general form of a vertical translation?

Back

The general form of a vertical translation is g(x) = f(x) + c, where c is a constant.

Front

What is the general form of a horizontal stretch?

Back

The general form of a horizontal stretch is g(x) = f(kx), where k is a constant.