Linear Transformations

Front

What is the linear parent function?

Back

y = x

Front

Describe the transformation from the graph of f to the graph of g if g is reflected and shifted down 2 units.

Back

Graph g is reflected and shifted down 2 units.

Front

What transformation occurs if f(x) = x is replaced with 2f(x)?

Back

Vertical stretch by a factor of 2

Front

Describe the transformation from the graph of f to the graph of g if g is shifted up 6 units.

Back

Graph g shifted up 6 units.

Front

What is the transformation of the parent function, f(x)=x, if k(x)=f(\frac{1}{3}x)?

Back

Less steep, Horizontal Stretch

Front

What is a linear transformation?

Back

A function that maps a vector space to itself, preserving the operations of vector addition and scalar multiplication.

Front

What is the effect of a vertical stretch on a function?

Back

It increases the distance of points from the x-axis by a specified factor.

Front

What does a horizontal compression do to a function?

Back

It decreases the distance of points from the y-axis by a specified factor.

Front

What is the general form of a linear function?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How does a negative sign in front of a function affect its graph?

Back

It reflects the graph across the x-axis.