NC Math 3 EOC Review

Front

What is an increasing function?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

How do you determine the intervals where a function is increasing?

Back

To find where a function is increasing, analyze the derivative of the function. If the derivative is positive on an interval, the function is increasing on that interval.

Front

What does the notation [a, b] represent in interval notation?

Back

The notation [a, b] represents a closed interval that includes the endpoints a and b.

Front

What is the absolute value function?

Back

The absolute value function, denoted as |x|, returns the non-negative value of x. It is defined as: |x| = x if x ≥ 0, and |x| = -x if x < 0.

Front

How do you write an absolute value inequality?

Back

An absolute value inequality can be written in the form |x - a| < b, which means that x is within b units of a.

Front

What is the solution to the inequality |x - 30| ≤ 2?

Back

The solution to the inequality |x - 30| ≤ 2 is the interval [28, 32].

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

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

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic function in standard form y = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).