Math 3 Fall Final Review

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which the function evaluates to zero, meaning the graph of the function intersects the x-axis.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, you can factor the polynomial and set each factor equal to zero, or use the Rational Root Theorem and synthetic division.

Front

What is the significance of the factor (x+3) in a polynomial?

Back

The factor (x+3) indicates that -3 is a zero of the polynomial, meaning the polynomial will equal zero when x = -3.

Front

Define decreasing interval in the context of a function.

Back

A decreasing interval is a range of x-values over which the function's output values decrease as x increases.

Front

How do you determine the decreasing intervals of a function?

Back

To determine decreasing intervals, analyze the first derivative of the function; where the derivative is negative, the function is decreasing.

Front

What does it mean for a function to be fully factored?

Back

A function is fully factored when it is expressed as a product of its linear factors and irreducible polynomials.

Front

What is the difference between a linear function and a polynomial function?

Back

A linear function is a polynomial of degree 1, while a polynomial function can have degrees greater than 1, involving terms with x raised to higher powers.

Front

What is the inverse of a function?

Back

The inverse of a function reverses the input-output relationship, meaning if f(x) = y, then f^{-1}(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap the x and y in the equation and solve for y.

Front

What is the role of the discriminant in quadratic equations?

Back

The discriminant determines the nature of the roots of a quadratic equation: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.