Pre-Calculus Vocabulary Quiz 2

y=kx^n

y varies directly as the nth power of x can be modeled by the equation __________

y=kx/z

y varies directly as x and inversely as z can by modeled by the equation ____________

y=kx, constant

y varies directly as x can be modeled by the equation ________, where k is called the ___________

y=k/x

y varies inversely as x can by modeled by the equation ___________

y=kxz

y varies jointly as x and z can be modeled by the equation __________

a-bi

a+bi is a root of a polynomial with real coefficients, b≠0, then ______ is also a root of the equation

-b/2a, f(-b/2x), -b/2a, f(-b/2a)

Consider the quadratic function f(x) = ax^2 + bx + c, a≠0. If a>0, then f has a minimum that occurs at x= ________. This minimum value is ___________. If a<0, then f has a maximum value that occurs at x= __________. This maximum value is __________

divisor, quotient, remainder, dividend

After performing polynomial long division, the answer may be checked by multiplying the _________ by the ________, and then adding the ___________. You should obtain the __________

polynomial

All rational functions can be expressed as f(x)= (p(x))/(q(x)) where p and q are ___________ functions and q(x)≠0

root or solution

Every real zero of a polynomial function appears as a/an ___________ of the graph

n

If a polynomial equation is of degree n, then counting multiple roots separately, the equation has _____ roots

0, Intermediate Value

If f is a polynomial function and f(a) and f(b) have opposite signs, then there must be at least one value of c between a and b for which f(c)=_____. This result is called the ________________ Theorem.

n-1

If f is a polynomial function of degree n, then the graph of f has at most _________ turning points

turns around, crosses

If r is a zero of even multiplicity, then the graph touches the x-axis and _____________ at r. If r is a zero of odd multiplicity, then the graph ________ the x-axis at r.

false

T/F: A polynomial function with four sign changes must have four positive real zeros

true

T/F: Even-degree polynomial functions have graphs with the same behavior at each end

true

T/F: If the degree of the numerator of a rational function equals the degree of the denominator, then setting y equal to the ratio of the leading coefficients gives the equation of the horizontal asymptote

true

T/F: Odd-degree polynomial functions have graphs with opposite behavior at each end

false

T/F: Some polynomials functions of degree 2 or higher have breaks in their graphs

true

T/F: The graph of f(x) = (x-2)^2 + 1 opens upward

x-c

The Factor Theorem states that if f is a polynomial function and f(c)=0, then _________ is a factor of f(x)

n, 1

The Linear Factorization Theorem states that an nth-degree polynomial can be expressed as the product of a nonzero constant and _______ linear factors, where each linear factor has a leading coefficient of ______

the constant term a_0, the leading coefficient a_n

The Rational Zero Theorem states that if p/q is a rational zero of f (where p/q is reduced to lowest terms), then p is a factor of _______ and q is a factor of _______

f(c)

The Remainder Theorem states that if the polynomial f(x) is divided by x-c, then the remainder is _______

end, leading

The behavior of the graph of a polynomial function to the far left or the far right is called its ________ behavior, which depends on the _________ term

3, -2

The degree of the polynomial function f(x)=-2x^3(x-1)(x+5) is _____. The leading coefficient is _____

False

The domain of every rational function is the set of all real numbers

one more than

The graph of a rational function has a slant asymptote if the degree of the numerator is ________________ the degree of the denominator

true

The graph of the reciprocal f(x)=1/x has a break and is composed of two distinct branches

square root of -1, -1

The imaginary unit i is defined as i= __________, where i squared = _____

standard, parabola , (h,k), a>0, a<0

The quadratic function f(x)=(x-h)^2 + k, a≠0, is in ____________ form. The graph of f is called a/an __________ whose vertex is the point _________. The graph opens upward if __________ and opens downward if a __________

complex, imaginary, real

The set of all numbers in the form a + bi is called the set of all _________ numbers. If b is not equal to 0, then the number is also called a/an ____________ number. If b=0, then the number is also called a/an _________ number