polynomial functions
he plays edgar(smells too)
what is the form of a rational function?
p(x)/q(x)
vertical asymptotes are defined by....
line in the graph where lines do not cross(essentially separates the graph)
find all real zeros of the function f(x) = (x-2)(x^2+x+2)
2 and 1/2 + root 7i/1/2 - root 7i
what are bounds of zeros
dont matter
sketch a graph, concave down, zeros are 1(mult 2),4(mult 1), and -6(mult 1)
look like the mcdonalds logo/derricks favorite place
if n=m, how to find asymptotes
division of coefficients
what is a complex zero?
zero with a complex number
who is my worst brawl stars character?
8-bit
describe end behavior of a even concave up power function
as x goes to negative infinity, f(x) goes to infinity
as x goes to infinity, f(x) goes to infinity
when graph rational functions, what do we need to find?i
x-ints
domain
asymptotes
table of points
holes
asymptotes will be what form if n = m+1
use intermediate value theorem to figure out if there is a zero in the interval (1,2) x^6-2x^4+x^2-1
yes
use factor theorem to determine if (x-1) is a factor of f(x)=2x^3-2x^2+x-1
it is a factor
are the functions below a polynomial function?
f(x) = x^3(x^2+x-root 2)
g(x) = x^2-1/x^3+4
Yes
No
how to know which direction a function with two vertical asymptotes will go in the middle based off the line outside both asymptotes
same direction if even, opposite if odd
use descartes rule of signs to figure out how many potential zeros there are in the f(x) = x^3-2x^2+5x+2
2 or 0 potential positive zeros
1 potential negative zero
how many swim practices has derrick skipped without telling anyone?
2
multiplicities and effect on graphing polynomial functions?
cross if odd, touch if even
solve the inequality 5/x-3>3/x+1
i didn't feel like solving it so good job if u did
list all potential all rational zeros of f(x)=4x^3-2x^2-5x+18
1/2, 1, 18/4, 9/4, 9/2, 9, 18, 6, 3, 3/2, 3/4, 1/4
find the remainder of f(x)=x^3-3x^2+2 when divided by (x+2)
-18