Polynomial Functions
Rational Functions
Logarithmic Functions
Exponential Functions
Shhh!! It's A Secret
100
​For the quadratic function f(x)=-3x2-6x-5
​a. Write the quadratic function in standard form by completing the square.
b. State the vertex and y-intercept.​


a. f(x) = -3(x+1)2-2

b. Vertex: (-1, -2)    

    y-intercept: (0,-5)


100

Does the following function have a hole? If so, where?

f(x) = x2-x-2/x2+x-6

Yes! There is a hole.

x = 2

100
​​​Evaluate the following logarithmic exactly if possible, otherwise approximate with a calculator or explain why the logarithmic does not exist.

log100,log31/81,ein5
​log2(-8),log520​​​

-3, -4, 5, undefined, 1.8614

100
State the domain and range of the function
f(x) = e-x+1
​D:(-∞,∞)
R:(1,∞)​
100

True or False: An odd degree polynomial could have all imaginary zeros.

False!! Imaginary zeros come in pairs.

200
Divide the polynomial by the linear factor with synthetic division, indicating the quotient Q(x) and the remainder R(x).
17x5-4x3+2x-10/x+2

​Q(x) = 17x4-34x3+64x2-128x+258
R(x) = -526​
200
​Find the intercepts of the function:
f(x) = x2-x-2/x2+x-6​
​x-intercept: (-1,0)
y-intercept: (0,1/3)​
200
​State the domain and range of the function:
g(x) = log(x-3)+1​
​D:(3,∞)
R:(-∞,∞)​
200

Exponential function is the inverse of a _________________ function.

Logarithmic

200

True or False: The graph of a polynomial function might not have any x-intercepts.

True!!

300

f(x) = x3-13x+12

a. Determine the possible number of positive and negative real zeros.

b. Use the rational zero theory to determine the possible rational zeros.

c. Determine the zeros of the polynomial.

a. 2 or 0 positive real zeros, 1 negative real zero

b. ±1, ±2, ±3, ±4, ±6, ±12

c. zeros: -4, 1, 3

300
​Find the asymptotes of the function:
f(x) = x2-x-2/x2+x-6​
​VA: x = -3
HA: y = 1​
300
​Write the expression as a sum or difference of logarithms.
In[x2-x-6/x2+7x+6]​

In(x+2)+In(x-3)-In(x+1)-In(x+6)

300
Solve the equation exactly, otherwise, give an approximation:
5ex+12 = 27

x = In3 ~ 1.0986

300
​Solve the system of linear equations in two variables
5x+2y = 1
2x - 3y = -11​

(-1, 3)

400

A bookstore sells used textbooks to students. The profit of selling x textbook is given by f(x) = 5000 + 16x - 0.2x2
a. How many books should be sold to maximize the profit?
b. What is the maximum profit?

a. 40 books
b. Profit --> $5320
400
From the given information graph the following function
f (x) = x2-x-2/x2+x-6
Hole: x = 2
Intercepts: x - intercept: (-1, 0) , y-intercept: (0,1/3)
Asymptotes:  VA: x = -3 , HA: y = 1  

Plug-in function to desmos.

400
​Solve the equation exactly, otherwise, give an approximation:
In(x+8) = In (x) + In(x+3)​

x = 2

400

Your initial investment is $20,000 and the interest in an account is 5% how much will you have in the account in 10 years if the interest is compounded continuously?

Interest 10 years later: $32,974.43

400
Solve the system of linear equations in three variables
x + y + z = 0
2x + z = -1
x-y -z =2

(1, 2, -3)

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