Analyzing Functions and Transformations

Front

What is a transformation in the context of functions?

Back

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

Front

What does a horizontal shift of a function mean?

Back

A horizontal shift moves the graph of the function left or right along the x-axis.

Front

What does a vertical shift of a function mean?

Back

A vertical shift moves the graph of the function up or down along the y-axis.

Front

What is a vertical compression?

Back

A vertical compression occurs when the graph of a function is squeezed towards the x-axis, making it flatter.

Front

What is a vertical stretch?

Back

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

Front

How do you identify the vertex of a parabola in vertex form?

Back

In the vertex form f(x) = a(x-h)^2 + k, the vertex is the point (h, k).

Front

What is the minimum value of a quadratic function in vertex form?

Back

The minimum value occurs at the vertex if the parabola opens upwards (a > 0).

Front

What is the average rate of change of a function?

Back

The average rate of change of a function between two points is the change in the function's value divided by the change in the input value.

Front

How do you find the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.