Review Transformations 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 function, including translations, reflections, stretches, and compressions.

Front

What does it mean to translate a function left or right?

Back

Translating a function left or right involves shifting the graph horizontally. A positive value shifts it left, while a negative value shifts it right.

Front

What does it mean to translate a function up or down?

Back

Translating a function up or down involves shifting the graph vertically. A positive value shifts it up, while a negative value shifts it down.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|, which creates a V-shaped graph.

Front

How does the equation y = |x + 4| + 7 transform the parent function?

Back

This equation translates the parent function left 4 units and up 7 units.

Front

What is the effect of the coefficient in front of the absolute value function?

Back

The coefficient affects the vertical stretch or compression of the graph. A value greater than 1 stretches it, while a value between 0 and 1 compresses it.

Front

What transformation does g(x) = |x - 2| + 4 represent?

Back

This function is shifted right 2 units and up 4 units from the parent function.

Front

What is the transformation of f(x) = |x| to g(x) = |x - 2|?

Back

The transformation is a shift to the right by 2 units.

Front

How do you identify vertical and horizontal translations in a function?

Back

Vertical translations are indicated by constants added or subtracted outside the function, while horizontal translations are indicated by constants added or subtracted inside the function.

Front

What does the equation f(x) = 2|x - 2| - 3 represent?

Back

This equation represents a vertical stretch by a factor of 2, a shift right 2 units, and a shift down 3 units.