AA2 Analyzing Functions

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values where the function's output (y-values) rises as x increases.

Front

How do you determine the increasing interval of a quadratic function?

Back

For a quadratic function in the form f(x) = ax^2 + bx + c, the increasing interval is found by determining the vertex and analyzing the direction of the parabola. If a > 0, the function increases after the vertex.

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a range of x-values where the function's output (y-values) falls as x increases.

Front

How do you find the decreasing interval of a quadratic function?

Back

For a quadratic function f(x) = ax^2 + bx + c, the decreasing interval is before the vertex if a > 0.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output value is produced by exactly one input value, meaning it passes the horizontal line test.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one by checking if any horizontal line intersects the graph more than once.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at x = -b/(2a) for the function f(x) = ax^2 + bx + c.

Front

What is the significance of the vertex in determining intervals?

Back

The vertex helps identify where the function changes from increasing to decreasing or vice versa.

Front

What is the general form of a quadratic function?

Back

The general form is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the intervals of increase and decrease for a function?

Back

To find intervals of increase and decrease, calculate the derivative of the function, set it to zero to find critical points, and test intervals around those points.