I'm being totally rational!
What's the y-intercept of:
r(x)=\frac{x^2+6}{2x^2+7x-3}
(0,-2)
x2 - 169 factors into...
(x+13)(x-13)
What is the vertex of
f(x) = 2(x-4)^2 - 5?
Vertex = (4,-5)
What is the value of "c" in x+4?
c = -4
What is a "zero" of a function f(x)?
A value of x that makes f(x)=0.
(Also an x-intercept!)
What's the horizontal asymptote of:
r(x) = \frac{5x^2}{3x^2-10x+2}
y = \frac{5}{3}
5x2 + 20x + 15 factors into...
5(x+3)(x+1)
Where does f(x) = -(x+3)^2 + 4 have a minimum or maximum?
Maximum at x = -3
If 5 is a zero, what is it's corresponding factor?
(x - 5)
What is the zero of f(x) = 12+x ?
zero = -12
What's the vertical asymptote(s) of:
r(x)=\frac{7}{x^2-64}
x = -8, 8
x2 + 25 factors into...
(x+5i)(x-5i)
Put f(x) = x^2 - 2x + 3 into standard form.
f(x) = (x-1)^2 + 2
What type(s) of polynomial division could you use to divide P(x) = 2x^4 - 5x^3 + x - 10 by D(x) = x - 2 ?
Synthetic or long division
Find all the zeros of
f(x) = x^2 + 81
zeros = -9i, 9i
What are the x-intercepts of:
r(x)=\frac{4x^2+8x-60}{x^2+17}
(-5,0) and (3,0)
Factor P(x) = x^4 - 8x^2 - 9
into its linear and irreducible quadratic factors with real coefficients.
(x2+1)(x+3)(x-3)
DAILY DOUBLE!
Find the maximum value of the function and where it occurs
f(x) = 20x - 0.5x^2 .
Maximum value = 200
@ x = 20
What type(s) of polynomial division could you use to divide P(x) = -6x^3 + 8x^2 - 3x - 1 by D(x) = x^2 - 1 ?
Long division
Find all the zeros of
f(x) = x^4 - 16
zeros: -2, 2, -2i, 2i
Find the slant asymptote of the rational function:
r(x)=\frac{x^2-9x+17}{x-4}
y=x-5
Factor P(x) = x^4 - 8x^2 - 9
completely into its linear factors with complex coefficients.
(x+i)(x-i)(x+3)(x-3)
Find the x- and y-intercepts of
f(x)=-x^2+8x
x-intercepts: (0,0) and (8,0)
y-intercept: (0,0)
Divide P(x) = 3x^2 - 7x + 11 by D(x) = x-3 . Find the quotient and the remainder.
Q(x) = 3x + 2
and
R(x) = 17
What's the complete factorization of
f(x)=x^4-16?
f(x)=(x+2)(x-2)(x+2i)(x-2i)