MVP Module 3 Review

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

What is the domain of the function f(x) = x^2 - 3?

Back

The domain is (-∞, ∞) because any real number can be squared.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than at the first.

Front

Determine the increasing interval of the function f(x) = -x^2 + 4.

Back

The function is increasing on the interval (-∞, 0).

Front

What is 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 is the range of the function f(x) = -x^2 + 4?

Back

The range is (-∞, 4] because the maximum value is 4 when x = 0.

Front

What is a maximum height in the context of a function?

Back

The maximum height refers to the highest point on the graph of a function, often found at the vertex of a parabola.

Front

What is the maximum height of the function f(x) = -x^2 + 200?

Back

The maximum height is 200, occurring at x = 0.

Front

What is an interval in mathematics?

Back

An interval is a range of numbers between two endpoints, which can be open or closed.

Front

What is the difference between open and closed intervals?

Back

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