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 functions?

Back

f(x) = x

Front

How does the equation y = f(x) + k transform the graph of f(x)?

Back

The graph shifts vertically by k units; if k is positive, it shifts up, and if k is negative, it shifts down.

Front

How does the equation y = f(x - h) transform the graph of f(x)?

Back

The graph shifts horizontally by h units; if h is positive, it shifts right, and if h is negative, it shifts left.

Front

What effect does multiplying the function by a positive constant have?

Back

It vertically stretches the graph if the constant is greater than 1, and compresses it if the constant is between 0 and 1.

Front

What is the effect of a negative sign in front of the function, such as y = -f(x)?

Back

It reflects the graph across the x-axis.

Front

If the equation is y = f(x) + 3, how does the graph shift?

Back

The graph shifts up 3 units.

Front

If the equation is y = f(x - 2) + 1, describe the transformations.

Back

The graph shifts right 2 units and up 1 unit.

Front

What does the term 'vertical stretch' mean in the context of linear transformations?

Back

A vertical stretch occurs when the output values of the function are multiplied by a factor greater than 1, making the graph taller.

Front

What does the term 'horizontal compression' mean?

Back

A horizontal compression occurs when the input values of the function are multiplied by a factor greater than 1, making the graph narrower.