5.6 Transforming Linear Equations

Front

What is the parent function of linear equations?

Back

The parent function of linear equations is f(x) = x.

Front

How does the slope of a linear equation affect its steepness?

Back

A larger absolute value of the slope indicates a steeper line, while a smaller absolute value indicates a less steep line.

Front

What transformation occurs when a linear function is shifted up by a certain number of units?

Back

The transformation is described as the graph being shifted UP by that number of units.

Front

If a linear equation has a slope of 5, how does it compare in steepness to the parent function?

Back

The equation y = 5x is STEEPER than the parent function y = x.

Front

What is the effect of a slope of 1/3 on the steepness of a linear graph compared to the parent function?

Back

The equation y = (1/3)x is LESS STEEP than the parent function y = x.

Front

What does it mean for a linear function to be transformed vertically?

Back

Vertical transformation refers to shifting the graph up or down along the y-axis.

Front

How can you determine if one linear equation is steeper than another?

Back

Compare the absolute values of their slopes; the one with the larger absolute value is steeper.

Front

What is the transformation when the function g(x) = f(x) + 4 is applied to the parent function?

Back

The graph of g(x) is shifted UP 4 units from the parent function.

Front

What happens to the graph of a linear function when the slope is negative?

Back

The graph will slope downwards from left to right.

Front

How do you identify a vertical shift in a linear equation?

Back

A vertical shift is identified by a constant added or subtracted from the function, such as g(x) = f(x) + k.