Algebra II - Fall Final

Concepts

100

Name every set that this number belongs to.

1/2

Real, Rational

200

This polynomial is a cubic binomial.

ex.    x³ + 3

300

What is the vertex and general form of a quadratic equation?

general: y=ax²+bx+c

vertex: y-k=a(x-h)

400

In a logarithm, why is it that the base of the logarithm must be greater than zero?

You may use an example to demonstrate. 

ex. log_-2y=1/2

then, -2^1/2=y.

Then y is imaginary.

500

What is the closure axiom and how does the axiom pertain to functions and polynomials?

Closure Axiom: For all real numbers, if you add or multiply a real number to another real number, then your product or sum will also be a real number.

Polynomials must be closed in order to be a polynomial. All polynomials are functions and their graphs have no holes.

Functions

100

Plot 3 points from the equation: y²=x+1. Is this a function? Why or why not?

It is not a function. Using the vertical line test, we can see that there exist more than one dependent variable for multiple independent variables in the domain.

200

What is the range of the following function:

y = x - 1 where the domain is {x| -1 < x < 4}

Range: {y| -2 < y < 3}

300

Solve the following equation:

x²-14x+50=0

x= 7+i, 7-i

400

Put the following function in vertex form and tell it's vertex:

y = x²+8x+21

y-5=(x+4)²

^{Vertex: (-4,5)}

500

If f(x)=3x²+2x-11, find x, when f(x)=-6

x=1, x=-5/3

Algebra

100

Graph the inequality:

y+4<6

y<2

<---------------------o(2)

200

Solve the inequality and graph it on a number line:

2 - 5x < 17

x>-3

300

Solve the inequality: |x+4| > 2. Graph your answer on a number line.

x<-6 or x>-2

<-----------0(-6)                 0(-2)---------------->

400

Simplify the expression:

7[2 - 3 (x - 4) + 4 (x - 6)]

7x-70

500

Solve and graph the inequality.

|3 - 4x|<9

x > -3/2

x < 3

Misc.

100

Plot y= -3x+4 using your knowledge of slope and y-intercepts.

In class.

200

Find the discriminant and tell if the solution will be real or imaginary:

-2x²+6x-7=-5

D: 20

Real solutions!!

300

Perform the indicated operation:

(2i)⁴+(5+i)

21+i

400

Find the slope of the linear function that contains the points: (1,4) and (3,8).

Slope = 2

500

Solve the system of equations:

3x+10y=-24

6x+7y=-9

x=2, y=-3

Exponent +Log

100

Find the exact value:

8^2/3

4

200

Solve for x: 

log₄x=3

x=64

300

Simplify:

(2x)^-5 / (4x²)^-2

1/(2x)

400

Solve for x:

8 * 5^3x = 16

x = 0.1426

log(2) / (3(log(5)) =x

500

If log 5 ~ 0.699 and log 3 ~ 0.477, find log (45) without using "log" in calculator! (SHOW WORK FOR POINTS)

log (45) = log (3*3*5) = log (3) + log (3) + log (5)  

=1.653