Identify Function Transformations

Front

What is the transformation of the function f(x)=x^3 when it is shifted three units left?

Back

The transformed function is (x + 3)^3.

Front

How do you represent the transformation of the function f(x)=(x - 4)^2 when it is reflected over the x-axis and shifted up 3 units?

Back

The transformed function is f(x)=-(x - 4)^2 + 3.

Front

What is the transformation of the function f(x)=√x when it is reflected over the x-axis?

Back

The transformed function is g(x)=-√x.

Front

What is the transformation of the function f(x)=x^3 when it is shifted four units down?

Back

The transformed function is x^3 - 4.

Front

What is the transformation of the function f(x)=x^2 when it is shifted three units to the right?

Back

The transformed function is g(x)=(x - 3)^2.

Front

What does it mean to shift a function to the left?

Back

Shifting a function to the left means adding a positive value to the x variable inside the function.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means multiplying the entire function by -1.

Front

How do you shift a function up?

Back

To shift a function up, you add a positive value to the entire function.

Front

What is the effect of adding a constant to the x variable in a function?

Back

Adding a constant to the x variable shifts the function horizontally.

Front

What is the effect of subtracting a constant from the function?

Back

Subtracting a constant from the function shifts it vertically down.