Graph Transformations and Parent Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (y = x), quadratic functions (y = x^2), and absolute value functions (y = |x|).

Front

What transformation occurs when a function is translated left?

Back

When a function is translated left, the x-coordinates of all points on the graph are decreased by a certain value. For example, the function y = (x + 4)^2 is the parent function y = x^2 translated left by 4 units.

Front

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

Back

A negative sign in front of a quadratic function reflects the graph across the x-axis. For example, y = -x^2 opens downwards instead of upwards.

Front

How do you identify a linear function?

Back

A linear function can be identified by its constant rate of change, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean to compress a graph vertically?

Back

To compress a graph vertically means to reduce the distance between points on the graph towards the x-axis. For example, y = (1/2)x^2 compresses the parent function y = x^2 by a factor of 1/2.

Front

What is the transformation of the function y = (x - 3)^2?

Back

The function y = (x - 3)^2 is the parent function y = x^2 translated right by 3 units.

Front

What does the absolute value function look like?

Back

The absolute value function, y = |x|, has a V-shape and reflects all negative y-values to positive, making it non-negative for all x.

Front

What is the transformation of the function y = |x + 2|?

Back

The function y = |x + 2| is the parent function y = |x| translated left by 2 units.

Front

How do you shift a graph up?

Back

To shift a graph up, you add a constant value to the function. For example, y = x^2 + 3 shifts the graph of y = x^2 up by 3 units.

Front

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

Back

A horizontal shift moves the graph left or right. For example, y = (x - 5)^2 shifts the graph of y = x^2 right by 5 units.