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 both endpoints a and b.

Front

What is the absolute value function?

Back

The absolute value function, denoted as |x|, gives the distance of x from 0 on the number line, always resulting in a non-negative value.

Front

How do you express a range of values using absolute value?

Back

To express a range of values using absolute value, use the form |x - a| ≤ b, which indicates that x is within b units of a.

Front

What is the significance of the manufacturer's recommended tire pressure?

Back

The manufacturer's recommended tire pressure is the optimal pressure for safety and performance, ensuring the tire functions correctly.

Front

How do you model a situation with an absolute value inequality?

Back

To model a situation with an absolute value inequality, set up the inequality in the form |x - a| ≤ b, where a is the target value and b is the allowable deviation.

Front

What does it mean if a function is decreasing on an interval?

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 difference between a closed interval and an open interval?

Back

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

Front

How do you find the critical points of a function?

Back

Critical points are found by setting the derivative of the function equal to zero and solving for x, as well as identifying points where the derivative does not exist.