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 of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by the value of b in the function f(x) = mx + b.

Front

How does changing the slope of a linear function affect its graph?

Back

Changing the slope 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 happens to the graph of f(x) = x when you subtract a constant from it?

Back

Subtracting a constant from f(x) = x shifts the graph downward by that constant value.

Front

If the slope of a linear function is increased, what can be said about the graph?

Back

If the slope is increased, the graph becomes steeper.

Front

What does it mean to translate a graph vertically?

Back

Translating a graph vertically means shifting the entire graph up or down without changing its shape.

Front

What is the effect of changing the y-intercept of a linear function?

Back

Changing the y-intercept shifts the graph up or down along the y-axis, affecting where the graph crosses the y-axis.

Front

How do you determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if its slope is positive and decreasing if its slope is negative.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope but different y-intercepts.