Transformations of Parent 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, including shifts, stretches, compressions, and reflections.

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 to the left, while a negative value shifts it to the 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 a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

How do you reflect a function over the x-axis?

Back

To reflect a function over the x-axis, you multiply the entire function by -1, which flips the graph upside down.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x², which is a parabola that opens upwards.

Front

How do you write the equation of a quadratic function translated left 4 units?

Back

The equation of a quadratic function translated left 4 units is y = (x + 4)².

Front

What is the effect of a vertical stretch by a factor of 5 on the parent function f(x) = x²?

Back

The effect of a vertical stretch by a factor of 5 on f(x) = x² is g(x) = 5x², which makes the parabola narrower.

Front

What does the equation y = -x² + 2 represent?

Back

The equation y = -x² + 2 represents a quadratic function that is reflected over the x-axis and shifted up 2 units.