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 does it mean for a function to be 'steeper'?

Back

A function is considered 'steeper' if its slope is greater than that of another function, meaning it rises or falls more quickly.

Front

What is the parent function of a linear equation?

Back

The parent function of a linear equation 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 the constant term in the equation. For example, shifting up by 5 units adds 5 to the constant term.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph over the x-axis.

Front

What does it mean for a graph to be parallel?

Back

Two graphs are parallel if they have the same slope but different y-intercepts.

Front

How do you determine the slope of a linear function from its equation?

Back

The slope of a linear function in the form y = mx + b is given by the coefficient m.

Front

What happens to the graph of f(x) = mx + b when m is increased?

Back

When m is increased, the graph becomes steeper.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.