Linear Transformations

Front

What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

Front

What is the parent function of linear equations?

Back

The parent function of linear equations is f(x) = x, which represents a straight line with a slope of 1.

Front

How does shifting a graph vertically affect its equation?

Back

Shifting a graph vertically affects its equation by adding or subtracting a constant from the function. For example, shifting down by 7 units results in f(x) = x - 7.

Front

What does it mean for a line to be steeper?

Back

A line is steeper if it has a greater absolute value of slope. For example, a line with a slope of 3 is steeper than a line with a slope of 2.

Front

How do you determine if one line is less steep than another?

Back

To determine if one line is less steep than another, compare their slopes. The line with the smaller absolute value of slope is less steep.

Front

What is the effect of multiplying a function by a scalar?

Back

Multiplying a function by a scalar affects the steepness of the line. For example, g(x) = ⅓f(x) makes the line less steep than f(x) = x.

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x) - 6?

Back

The graph of f(x) = x is shifted down 6 units when transformed to g(x) = f(x) - 6.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope of a line from its equation?

Back

The slope of a line can be identified from its equation in slope-intercept form (y = mx + b) as the coefficient of x (m).

Front

What does it mean for a function to be transformed?

Back

A function is transformed when it is altered in some way, such as shifting, stretching, or reflecting, which changes its graph.