ANY EQUATION OR FUNCTION THAT IS LINEAR WILL ONLY HAVE X ____ ____ ___ ____ ____.
RAISED TO THE FIRST POWER.
EX: f(x) = 2x - 7
NO ABSOLUTES, NO EXPONENTS, ONLY TO THE FIRST POWER.
WHAT DOES A QUADRATIC AND ABSOLUTE POWER GRAPHS LOOKS LIKE?
NON LINEAR!
WHAT DOES A CUBIC AND SQUARE ROOT FUNCTION LOOK LIKE ON A GRAPH?
NON LINEAR !
HOW DO YOU WORK WITH A NEGATIVE EXPONENT?
EX: 2-4
RECIPROCATE!
2-4 = 1/24 = 1/16 = .0625
OR IF YOUR WORKING WITH IT IN A DIVISION PROBLEM USE THE FRACTION.
EX:-20/ 2-4
=-20/1 * 1/ 24 = -20/ 16
=-1.25
43 donate 81.00
21 donate 75.00
16 donate 100.00
QUESTION: WHAT IS THE AVERAGE DONATION PER PERSON?
(43*81) + (21*75) + (16*100)
------------------------------------
43 + 21 + 16
THE TAKE HOME HERE IS THAT THE QUESTION ASKED FOR THE AVERAGE PER PERSON. NOTICE HOW YOU ADDED ALL IN THE DENOMINATOR.
IF YOU JUST DIVIDED BY 3 THAT WOULD GIVE YOU THE AVERAGE OF THE DONATIONS, NOT THE PER PERSON'S DONATION.
-102 AND (-10)2
WHAT IS THE DIFFERENCE AND HOW DO YOU KNOW?
-102 = -(10 * 10) = -100
(-10)2 = (-10) * (-10) = 100
THINK OF IT THIS WAY: THE EXPONENT IS GOING GOING TO EFFECT WHAT IS ONLY NEXT TO IT. THE () HOLD EVERYTHING.
WITH THEM YOU CAN ONLY WORK WITH THE NUMBER AND NOT THE SIGN IN FRONT OF IT.
55 % IS FEMALE BUY PRODUCT X. WHAT IS THE RATIO OF FEMALE TO MALE WHO BUY PRODUCT X?
A.
55 FEMALE MEANS 45 MALE.
NOW DIVIDE TO FIND RATIO.
55/5 = 11 AND 45/5 = 9
YOUR RATIO IS 11:9.
MUST DIVIDE EVENLY.
AREA OF A RECTANGLE FORMULA.
Area = w × h
Example: A rectangle is 6 m wide and 3 m high, what is its Area?Area = 6 m × 3 m = 18 m2
PREIMETER OF A RECTANGLE FORMULA
Perimeter = 2(w+h)
Example: A rectangle has a width of 12 cm, and a height of 5 cm, what is its Perimeter?
Perimeter
= 2 × (12 cm + 5 cm)
= 2 × 17 cm
= 34 cm
HOW DO YOU READ THIS?
WHERE WOULD IT BE ON A GRAPH?
f(f(-1))
THINK OF IT THIS WAS. F=Y AND IT WILL TELL YOU THIS VIA THE X, WHICH IS IN THE ().
THE -1 IS ON THE X AXIS.
FOLLOW THIS UP TO THE POINT ON THE Y AXIS. f(f(-1)).
THIS GIVES YOU f(2).
DO THE SAME THING WITH f(2). GOTO 2 ON THE X AXIS AND FOLLOW IT UP TO THE Y COORDINATE, HERE IS 1.
d - 3n 7n - d =1
WHAT IS D IN TERMS OF N?
THE WHOLE EQUATION IS = 1.
SO THE NUMERATOR & DENOMINATOR ARE EQUAL.
SET NUM=DOM AND SOLVE FOR N. BECAUSE THAT IS WHAT THE QUESTION ASKS FOR "IN TERMS OF".
ANS IS D= 5N. OR "5 TIMES N".
Quantity A
Quantity B
x
y
(A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given.
If then so in this case, but if then so in that case,
Thus, the correct answer isChoice D,the relationship cannot be determined from the information given.
Quantity A
Quantity B
y
(B)
Y IS SMALLER BECAUSE IT IS BEING DIVIDED IN A.
Quantity A
Quantity B
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Set up the initial comparison:
Then simplify:
Step 1: Multiply both sides by 2 to get
Step 2: Add to both sides to get
Step 3: Simplify the right-hand side using the fact that to get
The resulting relationship is equal to (=). In reverse order, each simplification step impliesequal to in the preceding comparison. So Quantities A and B are also equal. Thus, the correct answer is Choice C, the two quantities are equal.
ADD THIS TOGETHER:
(-3)2 AND -32
(-3)2 = (-3)(-3) = 9
-32 = -(3 *3) = -9
Note that without the parentheses, the expression means “the negative of ‘3 squared’ that is, the exponent is applied before the negative sign.
T OR F
All positive numbers have two square roots, one positive and one negative.
