Analyzing Graphs

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

How do you express a domain in interval notation?

Back

In interval notation, the domain is expressed using brackets and parentheses to indicate whether endpoints are included or excluded. For example, the domain from -2 to infinity is written as [-2, ∞).

Front

What does an increasing interval on a graph indicate?

Back

An increasing interval on a graph indicates that as the x-values increase, the y-values also increase.

Front

What does a decreasing interval on a graph indicate?

Back

A decreasing interval on a graph indicates that as the x-values increase, the y-values decrease.

Front

How do you identify increasing and decreasing intervals from a graph?

Back

To identify increasing and decreasing intervals, look for sections of the graph where the slope is positive (increasing) or negative (decreasing).

Front

What is interval notation for the inequality -8 ≤ x < 8?

Back

The interval notation for -8 ≤ x < 8 is [-8, 8).

Front

What is the difference between closed and open intervals?

Back

A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not include its endpoints (e.g., (a, b)).

Front

How do you find the domain of a function from its graph?

Back

To find the domain from a graph, identify the x-values for which the graph exists and is defined.

Front

What is the significance of the endpoints in interval notation?

Back

Endpoints in interval notation indicate whether the values at those points are included (using brackets) or excluded (using parentheses).

Front

What is a critical point in the context of graph analysis?

Back

A critical point is where the function's derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.