Unit 3b test

Question 1

a. What does it mean if the lead coefficient is positive?
b. and negative?
c. What is this used for most commonly?

Answer 1

A
a. If positive the right most end goes up
b. If negative the right most end goes down
c. Sketching graphs and end behavior THIS APPLYS TO POLYNOMIAL FUNCTIONS TOO

Question 2

a. What does it mean if the power is even?
b. and odd?
c. What is this used for most commonly?

Answer 2

a. Even the left end goes in the same direction as the right one
b. Odd the left most end goes in the opposite direction as the right most one
c. Sketching graphs and end behavior THIS APPLYS TO POLYNOMIAL FUNCTIONS TOO

Question 3

How do you find the possible rational zeroes of this equation?: x^3-21x+20

Answer 3

do all factors of 20 as numerator and all factors of 1 as denominator each of those are a possible zero then use synthetic substitution to find if its an actual zero or not

Question 4

If you have a factor of
3+4i what do you know is also a factor

Answer 4

3-4i

Question 5

given the equation 2x-4/x + 1 with p(x) representing the numerator and q(x) representing the denominator
how do you find the
a. domain and range?
b. x and y intercepts
c. holes

Answer 5

a. you find the domain by knowing what makes the denominator 0, the range depends on the equation
b. for x you use the simplified version of the equation and set p(x)=0 for y you can use either the simplified or non-simplified version of the equation, and you set x=0 its also called f(0)
c. There are only holes if there is/are common factor(s) and even then only if you can cancel out all of said common factors. you find the x coordinate by using the non-simplified version of the equation and seeing what makes the denominator = 0 to find the y coordinate substitute the x coordinate number into the simplified version of the equation and what that equals is the y coordinate

Question 6

given the equation 2x-4/x + 1 with p(x) representing the numerator and q(x) representing the denominator
how do you find the
a. Horizontal asymptote
b. Vertical asymptote
c. Slant asymptote
d. How do you graph y = mx + b

Answer 6

a. if the degree of p > degree of q there is not HA.
if the degree of p < degree of q the asymptote is at y=0
If the degree of p is = degree of q then you find the horizontal asymptote by dividing the leading coefficient of p by the leading coefficient of q
b. in the simplified version of the equation set the denominator = 0
c. You can only have a SA if there is no HA and the degree of p has to be exactly one more that the degree off q if this is all true you find it by dividing p(x) by q(x) using synthetic or long division and ignoring the remainder (it should look like y = mx + b
d. m is the slope and b is the y intercept (remember rise over run)