Transformations of Parent Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

What transformation occurs when a function is reflected over the x-axis?

Back

The output values (y-values) of the function are multiplied by -1, flipping the graph upside down.

Front

How does the graph of y = (x - 2)^2 + 4 differ from the parent function y = x^2?

Back

It is translated right 2 units and up 4 units.

Front

What does it mean to stretch a function vertically?

Back

To stretch a function vertically means to multiply the output values by a factor greater than 1, making the graph taller.

Front

What is the effect of translating a function left 3 units?

Back

The entire graph of the function shifts 3 units to the left on the x-axis.

Front

How do you identify a quadratic function?

Back

A quadratic function can be identified by its standard form: y = ax^2 + bx + c, where a ≠ 0.

Front

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

Back

The graph is reflected over the x-axis and vertically stretched by a factor of 2.

Front

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

Back

It reflects the graph over the x-axis.

Front

How does the graph of y = x^2 + 5 differ from y = x^2?

Back

It is translated up 5 units.

Front

What does it mean to compress a function vertically?

Back

To compress a function vertically means to multiply the output values by a factor between 0 and 1, making the graph shorter.