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, which can include 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 a horizontal shift in function transformations?

Back

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

Front

What is a reflection in function transformations?

Back

A reflection flips the graph of the function over a specified axis, such as the x-axis or y-axis.

Front

What does a vertical stretch of a function mean?

Back

A vertical stretch occurs when the graph of a function is pulled away from the x-axis, making it taller.

Front

What does a vertical compression of a function mean?

Back

A vertical compression occurs when the graph of a function is pushed closer to the x-axis, making it shorter.

Front

How does the equation y = √(x - 5) + 4 transform the parent function y = √(x)?

Back

This equation reflects the graph horizontally right by 5 units and vertically up by 4 units.

Front

What is the effect of the coefficient 'a' in the function f(x) = a|x|?

Back

The coefficient 'a' affects the vertical stretch or compression of the graph. If |a| > 1, it stretches; if 0 < |a| < 1, it compresses.

Front

What does the equation g(x) = 5x² + 2 represent in terms of transformations from f(x) = x²?

Back

This represents a vertical stretch by a factor of 5 and a vertical shift up by 2.

Front

What is the parent function of f(x) = |x|?

Back

The parent function of f(x) = |x| is the absolute value function, which creates a V-shaped graph.