Transformations of Linear Functions

Front

What is the parent function of linear functions?

Back

f(x) = x

Front

How does the function f(x) = x - 2 transform the parent function?

Back

It shifts the graph down by 2 units.

Front

What transformation does g(x) = -f(x) represent?

Back

Reflection across the x-axis.

Front

How does the function y = f(x + 3) transform the parent function?

Back

It shifts the graph left by 3 units.

Front

What effect does replacing f(x) with 2f(x) have on the graph?

Back

It vertically stretches the graph by a factor of 2.

Front

How does the function y = f(x - 4) transform the parent function?

Back

It shifts the graph right by 4 units.

Front

What is the effect of adding a constant to the function, such as f(x) + 5?

Back

It shifts the graph up by 5 units.

Front

What transformation occurs when the function is multiplied by a negative number, such as g(x) = -f(x)?

Back

It reflects the graph across the x-axis.

Front

How does the function y = 0.5f(x) affect the graph of f(x)?

Back

It vertically compresses the graph by a factor of 0.5.

Front

What does the transformation f(x) = f(x - h) represent?

Back

A horizontal shift to the right by h units.