Algebra - Transformations (3.3)

Front

What is the linear parent function?

Back

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

Front

What does a vertical translation of a function involve?

Back

A vertical translation involves shifting the graph of the function up or down without changing its shape.

Front

If g(x) = f(x) - 3, how is the graph of g(x) related to f(x)?

Back

The graph of g(x) is shifted down 3 units from the graph of f(x).

Front

What is the effect of a vertical stretch factor of 2 on a function?

Back

A vertical stretch factor of 2 means that the output values of the function are multiplied by 2, making the graph steeper.

Front

How does the transformation g(x) = f(x) + 3 affect the graph of f(x)?

Back

The graph of g(x) is shifted up 3 units from the graph of f(x).

Front

What type of translation occurs when g(x) = f(x - 3)?

Back

This results in a horizontal translation to the right by 3 units.

Front

What is the difference between vertical and horizontal translations?

Back

Vertical translations shift the graph up or down, while horizontal translations shift the graph left or right.

Front

If g(x) = f(x) - 7, what type of transformation is this?

Back

This is a vertical translation downwards by 7 units.

Front

What happens to the graph of a function when it is vertically stretched?

Back

The graph becomes steeper, and the y-values increase more rapidly.

Front

How can you identify a vertical translation from a function's equation?

Back

A vertical translation can be identified by a constant added or subtracted from the function, such as f(x) + k or f(x) - k.