Transformations of Linear Functions 2

Front

What is a transformation of a linear function?

Back

A transformation of a linear function involves changing its position, shape, or size on a graph, which can include translations, reflections, stretches, and compressions.

Front

What does it mean to translate a function vertically?

Back

Translating a function vertically means shifting the graph up or down along the y-axis. For example, g(x) = f(x) + k translates the graph of f(x) up by k units if k > 0 and down if k < 0.

Front

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

Back

Reflecting a function over the x-axis means flipping the graph of the function upside down. This is represented by g(x) = -f(x).

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. For example, g(x) = af(x) where a > 1.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter. For example, g(x) = af(x) where 0 < a < 1.

Front

What does it mean to translate a function horizontally?

Back

Translating a function horizontally means shifting the graph left or right along the x-axis. For example, g(x) = f(x - h) translates the graph of f(x) right by h units if h > 0 and left if h < 0.

Front

How does the function g(x) = f(x) + 3 transform f(x)?

Back

The function g(x) = f(x) + 3 translates the graph of f(x) upward by 3 units.

Front

How does the function g(x) = f(x - 2) transform f(x)?

Back

The function g(x) = f(x - 2) translates the graph of f(x) to the right by 2 units.

Front

What is the effect of the function g(x) = -f(x) on the graph of f(x)?

Back

The function g(x) = -f(x) reflects the graph of f(x) over the x-axis.

Front

What does the function g(x) = 2f(x) do to the graph of f(x)?

Back

The function g(x) = 2f(x) vertically stretches the graph of f(x) by a factor of 2.