Big Review #3 (Passwater questions)

Front

What is the least possible degree of a polynomial function if it has a complex zero?

Back

The least possible degree of a polynomial function with a complex zero is at least 2, but if the polynomial has a complex zero of the form a + bi, it must also have its conjugate a - bi as a zero. Therefore, the minimum degree is 2 for each pair of complex conjugates.

Front

What is the behavior of a rational function near its vertical asymptotes?

Back

As the input values approach the vertical asymptote, the output values of the rational function can either increase or decrease without bound, depending on the direction from which the input approaches the asymptote.

Front

How do you determine the domain of a logarithmic function?

Back

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

The domain of a function is equal to the range of its inverse. If the function f has a domain of D, then its inverse function f^{-1} will have a range of D.

Front

What is the effect of the transformation y = f(x - h) + k on the graph of a function?

Back

The transformation y = f(x - h) + k shifts the graph of the function f horizontally by h units and vertically by k units. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function p(x) is a value x = a such that p(a) = 0. It represents the x-intercepts of the graph of the polynomial.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial expression. It determines the polynomial's end behavior and the maximum number of zeros it can have.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain. The overall function is defined by different expressions based on the input value.

Front

How do you find the inverse of a function graphically?

Back

To find the inverse of a function graphically, reflect the graph of the function across the line y = x. The resulting graph represents the inverse function.

Front

What is the definition of a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials, typically in the form r(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) ≠ 0.