Linear Function Transformations

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

Front

What effect does changing the slope of a linear function have on its graph?

Back

Changing the slope of a linear function affects the steepness of the graph. A larger slope value results in a steeper line, while a smaller slope value results in a less steep line.

Front

What does the y-intercept of a linear function indicate?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis. It represents the value of the function when x = 0.

Front

How does the graph of f(x) = x change when transformed to g(x) = f(x - c)?

Back

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

Front

How does the graph of f(x) = x change when transformed to g(x) = f(x + c)?

Back

The graph of f(x) = x shifts to the left by c units to create the graph of g(x) = f(x + c).

Front

What happens to the graph of a linear function when the output is multiplied by a fraction less than 1?

Back

When the output of a linear function is multiplied by a fraction less than 1, the graph becomes less steep.

Front

What happens to the graph of a linear function when the output is multiplied by a fraction greater than 1?

Back

When the output of a linear function is multiplied by a fraction greater than 1, the graph becomes steeper.

Front

What does the transformation g(x) = f(x) + k do to the graph of f(x)?

Back

The transformation g(x) = f(x) + k shifts the graph of f(x) vertically. If k is positive, the graph shifts up; if k is negative, the graph shifts down.

Front

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

Back

The transformation g(x) = f(x) - k shifts the graph of f(x) down by k units.