#8 AAE Transformations of Graphs

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a base for transformations. Examples include linear, quadratic, cubic, and absolute value functions.

Front

What transformation does the equation g(x) = (x - 1)^3 represent?

Back

This equation represents a horizontal shift of the parent cubic function to the right by 1 unit.

Front

What is the parent function of the quadratic equation y = (x + 2)^2?

Back

The parent function is the quadratic function, which is represented by y = x^2.

Front

What does the negative sign in front of the quadratic function y = -(x + 1)^2 indicate?

Back

The negative sign indicates a reflection of the graph across the x-axis.

Front

How does the equation y = (x - 2)^2 transform the parent function y = x^2?

Back

This equation represents a horizontal shift of the parent function to the right by 2 units.

Front

What is the effect of adding a constant outside the function, such as in y = x^2 - 3?

Back

Adding a constant outside the function shifts the graph vertically. In this case, the graph shifts down by 3 units.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the term 'transformation' refer to in graphing functions?

Back

Transformation refers to changes made to the graph of a function, including shifts, reflections, stretches, and compressions.

Front

What is the effect of a vertical stretch on the graph of a function?

Back

A vertical stretch occurs when the function is multiplied by a factor greater than 1, making the graph steeper.

Front

What is the parent function of a cubic equation?

Back

The parent function of a cubic equation is y = x^3.