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 over an interval, the function is increasing on that interval.

Front

What is the absolute value function?

Back

The absolute value function, denoted as |x|, measures the distance of x from 0 on the number line, always yielding a non-negative result.

Front

How do you express a range of values using interval notation?

Back

Interval notation uses brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints. For example, [2, ∞) includes 2 but not infinity.

Front

What does the notation |x - a| ≤ b represent?

Back

This notation means that the distance between x and a is less than or equal to b, indicating that x lies within the interval (a-b, a+b).

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. Maintaining pressure within the recommended range ensures proper tire function.

Front

How do you solve an absolute value inequality?

Back

To solve an absolute value inequality like |x - a| ≤ b, split it into two inequalities: a - b ≤ x ≤ a + b.

Front

What is the difference between an increasing function and a decreasing function?

Back

An increasing function rises as x increases, while a decreasing function falls as x increases.

Front

What does it mean for a function to be constant on an interval?

Back

A function is constant on an interval if it takes the same value for every point in that interval.

Front

How do you find the critical points of a function?

Back

Critical points occur where the derivative is zero or undefined. These points help determine intervals of increase or decrease.