Final Flashcards
log a C = B is equal to:
A^b = C
Ex: log x 1/64 = 2 is the same as:
X^2 = 1/64
or
x = +/- 1/8
How do you solve for: log a (MN)
Product log a (M) + log a (N)
How do you solve for: log a (M/N)
Quotient log a (M) - log a (N)
How do you solve for: log a M^p
Power
P log a M
ln C = B is the same as:
e^b = C
e^b = C is the same as:
Natural Log
ln C = B
Ex: e^9 = y is the same as:
ln y = 9
Find common bases:
9^x-4 = 27
3^2(x-4) = 3^3
Drop the bases
You get: 2(x-4) = 3
Solve: x = 11/2
i^2 =
-1
Ex: log base 9 of 11 - log base 9 of 8 =
11/8
Remember Quotient rules (M/N)
Ex: log base 2 of 5 + log base 2 of 7 =
log base 2 of 35
Remember Product rules (MN)
Ex: log base 6 of 1/25 =
-2 log base 6 of 5
because 5^-2 = 1/25
Ex: 3x^2 - 6x + 1 = 0
How will you solve?
Quadratic Formula using the rule:
ax^2 + bx + c = 0
-b +/- the square root of (b^2 -4ac) ALL over 2a
What do they mean when asking if a function is “one-to-one” ?
One-to-one means that no 2 point have the same y-coordinate
passes a horizontal line test
For graphing with Asymptotes you will:
Plug and chug with x = -2, -1, 0, 1, 2
What is the Factor Theorem
(x=c) is a factor if and only if P(c) = 0
What is the Rational Zeros Theorem
Ex: 5x^4 + 7x^3 +4x^2 +4x - 3
With any polynomial the values with x^power must be in descending order
- Number with x^ greatest power is a0 (or p)
- Number with no x is an (or q)
p/q = a combination of any factors of p or q individually
Ex: a0 = -3, an = 5
p/q = -3/5 …. factors of -3 are +/- 1 and +/- 3, factors of 5 are +/- 1 and +/- 5
Therefore the answer(s) are: +/- 1, +/- 3, +/- 1/5, +/- 3,5
Finds a line given to points
Ex: (5, -6) (-1, 3)
- Find slope (y2 - y1 / x2 - x1)
- Put in y = Mx + b, use one given set of points to plug in and solve for b
ex: (3) = -3/2(-1) + b
3/2 = b
Line: y = -3/2x + 3/2
Steps to graphing a Quadratic Function:
1 Does it have a Minimum or Maximum
- What x value does the min/max occur at
- What is the vertex
- If the Leading Coefficient is +, the graph will open UP and there will be a MINIMUM
To find the x calue and vertex:
x = - b / 2a
2x^2 - 4x + 1
Graph the quadratic function. Which way does it open and what is the vertex?
+ LC = opens UP
- LC = opens DOWN
x = - b /2a
Then plug and chug to find y-coord.
