Key Features of Graphs

Front

What is a maximum point on a graph?

Back

A maximum point is a point on the graph where the function value is greater than the values of the function at nearby points.

Front

What is a minimum point on a graph?

Back

A minimum point is a point on the graph where the function value is less than the values of the function at nearby points.

Front

How do you identify a relative maximum on a graph?

Back

A relative maximum can be identified where the graph changes from increasing to decreasing.

Front

How do you identify a relative minimum on a graph?

Back

A relative minimum can be identified where the graph changes from decreasing to increasing.

Front

What is a y-intercept?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, y).

Front

How do you find the y-intercept of a function?

Back

To find the y-intercept, set x = 0 in the function and solve for y.

Front

What does it mean if a graph has both a maximum and a minimum?

Back

It means the graph has points where it reaches both the highest and lowest values in certain intervals.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on its orientation.

Front

What is the difference between absolute and relative extrema?

Back

Absolute extrema are the highest or lowest points over the entire domain, while relative extrema are the highest or lowest points in a specific interval.

Front

What is the first derivative test?

Back

The first derivative test is used to determine whether a critical point is a relative maximum or minimum by analyzing the sign of the derivative.