REVIEW M3 Final Computer version

Front

What is the definition of the Least Common Denominator (LCD)?

Back

The Least Common Denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions.

Front

How do you find the vertical asymptote of a rational function?

Back

To find the vertical asymptote of a rational function, set the denominator equal to zero and solve for the variable.

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 point.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What are complex roots in a quadratic equation?

Back

Complex roots occur when the discriminant (b² - 4ac) of a quadratic equation is less than zero, resulting in roots that are not real numbers.

Front

How do you determine the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is an asymptote in mathematics?

Back

An asymptote is a line that a graph approaches but never touches or intersects.

Front

How do you identify the intervals of increase and decrease for a function?

Back

To identify intervals of increase and decrease, analyze the first derivative of the function: where f'(x) > 0, the function is increasing; where f'(x) < 0, it is decreasing.