Transformations of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope (m) of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

What is a vertical shift in the context of linear functions?

Back

A vertical shift occurs when a constant is added to or subtracted from a function. For example, f(x) + k shifts the graph up by k units if k > 0 and down by k units if k < 0.

Front

What is a horizontal shift in the context of linear functions?

Back

A horizontal shift occurs when the input variable (x) is adjusted by a constant. For example, f(x + h) shifts the graph left by h units if h > 0 and right by h units if h < 0.

Front

What does a vertical stretch of a linear function do?

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1. For example, g(x) = kf(x) where k > 1 stretches the graph vertically.

Front

What does a vertical shrink of a linear function do?

Back

A vertical shrink occurs when the output of the function is multiplied by a factor between 0 and 1. For example, g(x) = kf(x) where 0 < k < 1 shrinks the graph vertically.

Front

How does the equation g(x) = f(x) + 3 affect the graph of f(x)?

Back

The equation g(x) = f(x) + 3 shifts the graph of f(x) up by 3 units.

Front

How does the equation g(x) = 1/2f(x) affect the graph of f(x)?

Back

The equation g(x) = 1/2f(x) vertically shrinks the graph of f(x) by a factor of 1/2.

Front

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

Back

The equation g(x) = f(x - 4) shifts the graph of f(x) to the right by 4 units.

Front

What does the equation g(x) = -f(x) represent?

Back

The equation g(x) = -f(x) reflects the graph of f(x) across the x-axis.