Translating Linear Functions

Front

What is a vertical translation in the context of graph transformations?

Back

A vertical translation shifts the graph up or down without changing its shape.

Front

What does the equation k(x) = f(x) - 3 represent?

Back

A vertical translation of the graph of f down by 3 units.

Front

What is a horizontal translation in the context of graph transformations?

Back

A horizontal translation shifts the graph left or right without changing its shape.

Front

What does the equation m(x) = f(x + 2) represent?

Back

A horizontal translation of the graph of f left by 2 units.

Front

If f(x) = x + 6, what is the translated function for g(x) = f(x) - 8?

Back

g(x) = x - 2.

Front

What does the equation g(x) = f(x - 4) represent?

Back

A horizontal translation of the graph of f right by 4 units.

Front

If f(x) = -x + 4, what is the translated function for g(x) = f(x + 3)?

Back

g(x) = -x + 1.

Front

What is the effect of adding a positive number to the input of a function?

Back

It results in a horizontal translation to the left.

Front

What is the effect of subtracting a positive number from the output of a function?

Back

It results in a vertical translation down.

Front

How does the graph of f(x) = x transform to g(x) = f(x) + 5?

Back

The graph of f is translated vertically up by 5 units.