PRO Algebra

Question 1

x^m * x^n

Answer 1

x^(m+n)

Question 2

(x^m)^n

Answer 2

x^(m*n)

Question 3

x^0

Answer 3

1

Question 4

x^-m

Answer 4

1/x^m

Question 5

x^m / x^n

Answer 5

x^(m-n)

Question 6

What is the midpoint formula?

Answer 6

(x1+x2)/2, (y1+y2)/2

Question 7

What is the distance formula?

Answer 7

d=Square root of (x2-x1)^2 + (y2-y1)^2

Question 8

What is the quadratic formula?

Answer 8

-b +/- the square root of b^2 minus 4ac all over 2a

Question 9

(a^3 + b^3)

Answer 9

(a+b)(a^2-ab+b^2)

Question 10

(a^3 - b^3)

Answer 10

(a-b)(a^2+ab+b^2)

Question 11

a^2-b^2

Answer 11

(a-b)(a+b)

Question 12

a^3+3a^2b+3ab^2+b^3

Answer 12

(a+b)^3

Question 13

a^3-3a^2b+3ab^2-b^3

Answer 13

(a-b)^3

Question 14

What is the HA if the degree of the numerator is less than the degree of the denominator?

Answer 14

0

Question 15

What is the HA if the degree of the numerator is greater than the degree of the denominator?

Answer 15

DNE

Question 16

What is the HA if the degree of the numerator is equal to the degree of the denominator?

Answer 16

Ratio of leading coefficients

Question 17

What kind of symmetry exists if f(-x) is equal to f(x)?

Answer 17

Y-axis

Question 18

What kind of symmetry exists if f(-x) is equal to -f(x)?

Answer 18

Origin

Question 19

How do you find y-intercepts?

Answer 19

x=0

Question 20

How do you find x-intercepts?

Answer 20

y=0, only pay attention to numerator

Question 21

How do you find VA’s?

Answer 21

When the numerator equals a number, but the denominator is equal to 0

Question 22

How do you find slant asymptotes and how do you know if there will be one?

Answer 22

If the degree of the numerator is one more than the degree of the denominator, you can find a slant asymptote by dividing the numerator by the denominator (the remainder does not count)

Question 23

What is Ln a + Ln b?

Answer 23

Ln ab

Question 24

What is Ln a - Ln b?

Answer 24

Ln a/b

Question 25

Simplify Ln a^P

Answer 25

P times Ln a

Question 26

What is another form of logb(x)=C?

Answer 26

b^c=x

Question 27

Change logb(x) to natural logs

Answer 27

Ln x / Ln b

Question 28

What is the formula for continuously compounding interest?

Answer 28

P*e^rt

Question 29

What is the formula for interest compounded less than continuously?

Answer 29

P * (1+r/n)^nt

Question 30

Y is directly proportional to z

Answer 30

Y=kx

Question 31

Y is inversely proportional to x

Answer 31

Y=k/x

Question 32

Y is jointly proportional to x and n

Answer 32

Y=kxn

Question 33

What is the formula for a parabola?

Answer 33

Ax^2+Dx+Ey=0 or y=ax^2+bx+c change to y=a(x-h)^2+k, where vertex is (h,k) and 1/4a is the distance between the vertex and the focus or directrix In the regular form the x of the vertex is -b/2a

Question 34

What is the formula for a circle?

Answer 34

x^2+y^2+Dx+Ey+F or (x-h)^2+(y-k)^2=r^2 (h,k) is center, r is radius

Question 35

What is the formula for a ellipse?

Answer 35

Ax^2+Cy^2+Dx+Ey+F=0 Wide:(x-h)^2/a^2+(y-k)^2/b^2=1 Tall:(y-k)^2/a^2+(x-h)^2/b^2=1 The center is at (h,k), the a is distance right, the b is distance left, and the foci is c (a^2-c^2=b^2) units on the sides of the center

Question 36

What is the formula for a hyperbola?

Answer 36

``` Ax^2-Cy^2+Dx+Ey+F=0 Cupping y-axis:(x-h)^2/a^2-(y-k)^2/b^2=1 Cupping x-axis:(y-k)^2/a^2-(x-h)^2/b^2=1 Center:(h,k) Vertex is a from center Foci are c from center (c^2-a^2=b^2) Asymptotes are +/- b/a(x-h)+k or +/- a/b(x-h)+k ```

Question 37

How do you find the inverse of a function?

Answer 37

Switch the x and y

Question 38

What is the relationship between the domain and range of f^-1 related to f?

Answer 38

They switch

Question 39

If f and g are inverses what are f(g(x)) and g(f(x))?

Answer 39

x

Question 40

How do the graphs of f and its inverse relate?

Answer 40

The inverse is a reflection over y=x

Question 41

What is the requirement for a function to have an inverse?

Answer 41

It must be one to one, (passing both the vertical and horizontal line tests)

Question 42

What is i^2?

Answer 42

-1

Question 43

For an imaginary number a+bi, what is the real part and what is the imaginary part?

Answer 43

a,b

Question 44

What is the limit on "log"ing numbers?

Answer 44

You cannot log 0 or a negative number

Question 45

x^m/n

Answer 45

The n root of x^m

Question 46

What is the average rate of change of a function between two x-values?

Answer 46

The slope of the line connecting them, or Y2-Y1 over X2-X1

Question 47

What is gof?

Answer 47

The function f inserted as the x in function g