Transformations of Linear Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, which can include shifts, stretches, compressions, and reflections.

Front

What does a horizontal shift to the right by 'h' units look like in function notation?

Back

The function notation becomes f(x - h).

Front

What does a vertical shift up by 'k' units look like in function notation?

Back

The function notation becomes f(x) + k.

Front

What is the effect of a negative sign in front of a function?

Back

A negative sign reflects the graph of the function across the x-axis.

Front

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

Back

It shifts the graph of f vertically upward by k units.

Front

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

Back

It shifts the graph of f horizontally to the right by h units.

Front

What is the parent function of linear functions?

Back

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

Front

What does a vertical stretch by a factor of 'a' do to the graph of a function?

Back

It multiplies the output of the function by 'a', making the graph steeper if a > 1.

Front

What is the transformation represented by the equation y = -f(x)?

Back

It reflects the graph of f across the x-axis.

Front

What does the equation y = f(-x) represent?

Back

It reflects the graph of f across the y-axis.