Parent Functions and Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

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

Back

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller.

Front

What does a horizontal shift to the right by 2 units mean for the function f(x)?

Back

It means that the graph of the function f(x) is moved 2 units to the right along the x-axis, resulting in the transformation f(x - 2).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the parent function of a cubic function?

Back

The parent function of a cubic function is f(x) = x^3.

Front

What is the parent function of a linear function?

Back

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

Front

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

Back

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

Front

What is the effect of a vertical shift of +3 on a function?

Back

A vertical shift of +3 moves the graph of the function up 3 units.

Front

What is the effect of a horizontal compression by a factor of 1/2 on a function?

Back

A horizontal compression by a factor of 1/2 makes the graph of the function narrower.