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 slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What is the parent function of linear functions?

Back

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

Front

How does a positive slope affect the direction of a line?

Back

A positive slope indicates that the line rises from left to right.

Front

How does a negative slope affect the direction of a line?

Back

A negative slope indicates that the line falls from left to right.

Front

What does it mean to shift a function up or down?

Back

Shifting a function up means adding a constant to the output (y-values), while shifting down means subtracting a constant from the output.

Front

What is the effect of multiplying a function by a scalar greater than 1?

Back

Multiplying a function by a scalar greater than 1 stretches the graph vertically.

Front

What is the effect of multiplying a function by a scalar between 0 and 1?

Back

Multiplying a function by a scalar between 0 and 1 compresses the graph vertically.

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.

Front

What is the transformation represented by g(x) = f(x) - 4?

Back

This transformation represents a vertical shift down by 4 units.