Transformation of Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the parent function, which can include shifts, stretches, compressions, and reflections.

Front

What does it mean to stretch a function vertically by a factor of 3?

Back

Stretching a function vertically by a factor of 3 means that every y-coordinate of the function is multiplied by 3, making the graph taller.

Front

How does the equation f(x) = 3|x + 8| transform the parent function f(x) = |x|?

Back

The function stretches vertically by a factor of 3 and shifts left by 8 units.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function shifts the graph vertically. If the constant is positive, the graph shifts up; if negative, it shifts down.

Front

What does the equation y = x^2 + 5 represent?

Back

This equation represents a quadratic function that is the parent function y = x^2 shifted up 5 units.

Front

What transformation is represented by the equation y = (x + 4)^2?

Back

This equation represents a quadratic function that is the parent function y = x^2 shifted left 4 units.

Front

Describe the transformation of the function f(x) = (x - 3)^2 + 5 from the parent function f(x) = x^2.

Back

The function is shifted right 3 units and up 5 units from the parent function.

Front

What is the effect of a negative sign in front of a function?

Back

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

Front

How do you identify a vertical shift in a function?

Back

A vertical shift can be identified by the constant added or subtracted from the function's output (y-value).

Front

What does the term 'horizontal shift' refer to in function transformations?

Back

A horizontal shift refers to moving the graph left or right, determined by the value added or subtracted from the input (x-value).