prep for mobap test 2

Vertical asymptotes are found in the graphs of

• linear functions

• quadratic functions

• rational functions

• polynomial functions

the maximum or minimum value of a quadratic function occurs

• at the y intercept

• at an x intercept

• at the vertex

• they don't have maximums or minimums

Zeros of a rational function occur

• when a factor in the numerator equals zero

• when a factor in the denominator equals zero

• at a hole

• where the graph crosses a horizontal asumptote

The graph of a quadratic function

• is a straight line

• is a parabola

• is a circle

• is either always increasing or decreasing

The horizontal asymptote of

• y = 0

• y = 2

• y = 2x

• y = 2x + 3

a fourth degree polynomial

• can have as many as four zeros

• can have as many as 3 turning points

• has one y intercept

• can be written as a product of four linear factors

• all of the above are true

the rational root theorem is helpful in

• finding vertical asymptotes

• finding turning points

• finding a set of values that will include the zeros of a polynomial

• solving rational inequalities

a rational function could have a horizontal asymptote at y = 3 if

• the degree of its numerator is less than the degree of its denominator

• the degree of its numerator is the same as the degree of its denominator

• the degree of its numerator is greater than the degree of its denominator

Oblique asymptotes are found

• when the degree of the numerator of a rational function is one less than the degree of the denominator

• when the denominator and the numerator of a rational function are of the same degree

• when the degree of the numerator of a rational function is one greater than the degree of the denominator

• when a rational function has no vertical asymptotes

A zero of a polynomial function occurs at x = c

• when x - c is a factor of the polynomial

• when f(c) = 0

• when the remainder of f(x)/(x-c) is xero

• all of the above are true