# Thread: Pre-Calculus and what they mean ?

1. ## Pre-Calculus and what they mean ?

I've read some very informative, plain English definitions on the following Pre-Calc terms, but I still don't understand them and they are the following.

ABS (Absolute Value) Takes a single value and returns the positive version of it. Could anyone give me a easy to understand example.

Av, MIN & MAX - Correct me If I'm wrong but is MIN & MAX adjust where on a graph the curve should be, as for AV I have no clue

SQRT - Square Root takes a single value and calculates the square root of it. Could anyone give me a easy to understand example

Exponent: Pow (X,Y) This I don't understand.

I hope someone could help me understand the following terms.

2. Originally Posted by GreyWolf
ABS (Absolute Value) Takes a single value and returns the positive version of it. Could anyone give me a easy to understand example.
Suppose you are measuring altitude. You measure a hill, and it's 350 m tall. You measure another hill, and it's 150 m tall. You come to a valley. It's 75 m below your point of reference: you mark it down as being -75 m in altitude. If you jumped off the first hill to your reference point, you'd fall 350 m, the absolute value of the measurement. If you jumped from the reference point into the valley, you'd fall 75 m, the absolute value of the measurement.

You can think of absolute value as "distance from zero":

5 is 5 units away from zero.

-5 is also 5 units away from zero.

3. Originally Posted by GreyWolf
SQRT - Square Root takes a single value and calculates the square root of it. Could anyone give me a easy to understand example.
Square root asks "What number, multiplied by itself, equals the number I've been given?" Example:

SQRT(9) ... What number times itself equals 9? That would be 3.

SQRT(144) ... That would be 12. [Sorry for the gross example. ;-) ]

SQRT(2) ... gives an irrational number, 1.414....

4. Originally Posted by GreyWolf
Exponent: Pow (X,Y) This I don't understand.
This is normally pronounced in English as "to the".

3 "to the" 2nd power = $\displaystyle 3^2 = 3 \times 3 = 9$

2 to the 4th power = $\displaystyle 2^4 = 2 \times 2 \times 2 \times 2 = 16$

5. Originally Posted by GreyWolf
Av, MIN & MAX - Correct me If I'm wrong but is MIN & MAX adjust where on a graph the curve should be, as for AV I have no clue
I have no idea either. "Av" isn't really standard math notation. What actual definition does your book give?

6. You can think of absolute value as "distance from zero":

5 is 5 units away from zero.

-5 is also 5 units away from zero.
In other words you can start something from other then 0 (in relation to what I'm using it with) if I wanted to start something at 6 I would use Abs then 6, correct ?

Square root asks "What number, multiplied by itself, equals the number I've been given?" Example:

SQRT(9) ... What number times itself equals 9? That would be 3.

SQRT(144) ... That would be 12. [Sorry for the gross example. ;-) ]

SQRT(2) ... gives an irrational number, 1.414....
Square Root is how many times something can go into the number if it's even it will go in evenly if it's odd number it will give a decimal, correct?

This is normally pronounced in English as "to the".

3 "to the" 2nd power =

2 to the 4th power =
If you were to write something out, you could use $\displaystyle 4 to the power of 8$ which would mean 4x4x4x4x4x4x4x4 = 32 except writing out 4 to the power of 8 is more shorter way, correct?

7. Originally Posted by GreyWolf
In other words you can start something from other then 0 (in relation to what I'm using it with) if I wanted to start something at 6 I would use Abs then 6, correct ?
It sound like this might be a computer science class [?]. ABS is fixed as relative to zero. If you want fixed distance from a certain point, say 6, you'd first take the difference. Watch:

Consider the measurements 12, 6, and -3. Relative to zero, they are ABS(12) = 12, ABS(6) = 6, and ABS(-3) = 3.

Relative to a point x, they will be ABS(n - x). Therefore, if we measure relative to 6, they are ABS(12-6) = 6, ABS(6-6) = 0, ABS(-3-6) = 9.

Originally Posted by GreyWolf
Square Root is how many times something can go into the number if it's even it will go in evenly if it's odd number it will give a decimal, correct?
Nope. For SQRT(2), 2 is even, but SQRT gives 1.414...

And for 49, an odd number, SQRT(49) = 7, because $\displaystyle 7 \times 7 = 49$.

Originally Posted by GreyWolf
If you were to write something out, you could use $\displaystyle 4 to the power of 8$ which would mean 4x4x4x4x4x4x4x4 = 32 except writing out 4 to the power of 8 is more shorter way, correct?
True that $\displaystyle 4^8$ is shorter than writing a series of 8 fours multiplied together.

False that $\displaystyle 4^8$ is 32. That's addition. Multiplication gives 65536.

8. It sound like this might be a computer science class [?]. ABS is fixed as relative to zero. If you want fixed distance from a certain point, say 6, you'd first take the difference. Watch:

Consider the measurements 12, 6, and -3. Relative to zero, they are ABS(12) = 12, ABS(6) = 6, and ABS(-3) = 3.

Relative to a point x, they will be ABS(n - x). Therefore, if we measure relative to 6, they are ABS(12-6) = 6, ABS(6-6) = 0, ABS(-3-6) = 9.
It's a personal computer science class
I don't understand, yet. You say that ABS is relative to a point and in my example I have a line. If ABS(12-6) is 6 which I can understand you take away 6 from 12 and ABS(6-6) is 0 which I also can understand. If I have ABS(-5-8) is that -13 so my line would start -12 points down relative to 0 ?

Nope. For SQRT(2), 2 is even, but SQRT gives 1.414...

And for 49, an odd number, SQRT(49) = 7, because .
Right, because 2 is even also it can go into it's self once. If I had a number as in 43 that would cause a decimal, if I had a number as in 64 the SQRT would be 16, correct?

True that is shorter than writing a series of 8 fours multiplied together.

False that is 32. That's addition. Multiplication gives 65536.
Oh right, my mistake. What is floor and ceiling ?

9. Originally Posted by GreyWolf
It's a personal computer science class
I don't understand, yet. You say that ABS is relative to a point and in my example I have a line. If ABS(12-6) is 6 which I can understand you take away 6 from 12 and ABS(6-6) is 0 which I also can understand. If I have ABS(-5-8) is that -13 so my line would start -12 points down relative to 0 ?
ABS(-5-8) is 13, not -13.

Think of any two points on the number line. Subtract one from the other (order doesn't matter!) and then take the absolute value of the difference and that value is the distance between the points.

Example:

(1) Point A is at 8

(2) Point B is at -5

(3) -5-8=-13

(4) 8-(-5)=13

(5) ABS(-13)=13

(6) ABS(13)=13

Either way, the distance between the points is 13 units. This is why "absolute value" is also known as the "distance".

10. ABS is the distance between points, in other words how far the points are from each other ? ABS(12+4) what would that mean ? What are constants ?

11. Originally Posted by GreyWolf
ABS is the distance between points, in other words how far the points are from each other?
Yes. Watch this video and it will become very clear...

YouTube - College Algebra - Lecture 1 - Numbers

Originally Posted by GreyWolf
ABS(12+4) what would that mean?
16

(But keep in mind that - subtraction - is how the difference between points on the number line is calculated.)

Originally Posted by GreyWolf
What are constants?
A constant usually means a value that doesn't change or isn't allowed to change. (Context is important.) For example, in...

$\displaystyle E=MC^2$

The speed of light squared $\displaystyle C^2$ (in a vacuum) is a fixed constant. E and M are allowed to vary, but C is not. (Hence the names variables and constants.)

12. I still don't understand some things, I have yet to watch that video but I will

If a constant doesn't change, then what does the constants of the following mean?

TRUE, False, PI, E

What is ceiling, round, average, modulo

13. Originally Posted by GreyWolf
I still don't understand some things, I have yet to watch that video but I will

If a constant doesn't change, then what does the constants of the following mean?

TRUE, False, PI, E

What is ceiling, round, average, modulo
This was in "calculator discussion" so I suspect you are talking about abbreviations for a particular calculator. It would have helped if you had told us what calculator. Then we could just look them up in the manual for that calculator!

I believe that "AV" from you previous post is the arithmetic average of a list of numbers- for a list of, say 50 numbers, add them all together and divide by 50.

"True" and "False" are exactly what they say, the statement "x^2= 4" has value "True" when x has value 2 or -2, "False" otherwise.

PI is $\displaystyle \pi$, the ratio of the circumference of a circle to its diameter. It's an irrational number, about 3.141592.... "e" is the base of the natural logarithms, also irrational, about 2.7182818...... . On some calculators "E" is used differently. If a number is shown as "1.2433E4" that is 1.2433 times 10 to the Exponent 4 so is equal to $\displaystyle 1.2433 \times 10^4= 1.2433\times 10000= 12433$.

The "ceiling" of a number is the smallest integer larger than or equal to it. ceiling(1.00001)= 2, ceiling(1.999)= 2. "Floor" is the largest integer smaller than or equal to a number. floor(1.0001)= 1, floor(1.999)= 1. "Round" means to round off to the nearest integer. round(1.0001)= 1, round(1.999)= 2.

The "average" of a set of numbers is their "arithmetic average", the "AV" I mentioned before.

"modulo" requires two integers. Modulo(a, b) is the remainder when a is divided by b. Modulo(18, 6)= 2 because 6 divides into 20 3 times with remainder 2.

14. This was in "calculator discussion" so I suspect you are talking about abbreviations for a particular calculator. It would have helped if you had told us what calculator. Then we could just look them up in the manual for that calculator!
This was in calculator discussion, the question got cloned twice, probably my fault

I believe that "AV" from you previous post is the arithmetic average of a list of numbers- for a list of, say 50 numbers, add them all together and divide by 50.
I meant Absolute, which I'm still trying to understand ?

"True" and "False" are exactly what they say, the statement "x^2= 4" has value "True" when x has value 2 or -2, "False" otherwise.
I'm sorry, I don't understand what you mean ?

PI is , the ratio of the circumference of a circle to its diameter. It's an irrational number, about 3.141592.... "e" is the base of the natural logarithms, also irrational, about 2.7182818...... . On some calculators "E" is used differently. If a number is shown as "1.2433E4" that is 1.2433 times 10 to the Exponent 4 so is equal to .
Without breaking it down, Pi is Pie as in 3.14.

The "ceiling" of a number is the smallest integer larger than or equal to it. ceiling(1.00001)= 2, ceiling(1.999)= 2. "Floor" is the largest integer smaller than or equal to a number. floor(1.0001)= 1, floor(1.999)= 1. "Round" means to round off to the nearest integer. round(1.0001)= 1, round(1.999)= 2.
Ceiling (1.341)=1 ?
Floor (2.765)=3 ?
Round (2.753)=2 ?

"modulo" requires two integers. Modulo(a, b) is the remainder when a is divided by b. Modulo(18, 6)= 2 because 6 divides into 20 3 times with remainder 2.
Modulo(14,4)=2 remainder, because $\displaystyle 4 divided by 14$