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 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, [a, b] includes a and b, while (a, b) does not.

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 b units of a.

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 the form f(x) = 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).

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph. This means that for every x in the domain, f(x) is defined.