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 a function, including shifts, stretches, compressions, and reflections.

Front

What does a vertical shift of a function do?

Back

A vertical shift moves the graph of the function up or down without changing its shape.

Front

What is the effect of a horizontal shift on a function?

Back

A horizontal shift moves the graph of the function left or right.

Front

How does the equation f(x) = |x + 2| - 3 transform the parent function f(x) = |x|?

Back

It shifts the graph left 2 units and down 3 units.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x².

Front

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

Back

It represents a quadratic function that is shifted right 2 units and down 3 units from the parent function.

Front

How do you identify a vertical shift in a function?

Back

A vertical shift can be identified by a constant added or subtracted from the function, such as f(x) = x² + k.

Front

What is the transformation represented by the equation y = |x + 3| + 2?

Back

This equation represents a left shift of 3 units and an upward shift of 2 units from the parent function y = |x|.

Front

What does the term 'reflection' mean in function transformations?

Back

Reflection means flipping the graph of the function over a specific axis, such as the x-axis or y-axis.

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph over the x-axis.