General Questions About Functions?

Question

Please explain and answer each question given using simple words and not math jargon. I need to understand the FACTS in baby-like terms.

(1) Why does the letter y the same thing as writing f(x). In other words, why does y = f(x) and vice-versa?

(2) What is the basic difference the lines y = x and y = - x?

(3) Why do square root answers have a positive and negative result? Sample: sqrt{4} = +2 and -2. Why TWO answers?

(4) What is the most basic difference between the words DOMAIN and RANGE?

Answer 1

(1) Why does the letter y the same thing as writing f(x). In other words, why does y = f(x) and vice-versa?

y= f(x) because when you input a value into f(x) you get a corresponding y value.

(2) What is the basic difference the lines y = x and y = - x?

For y=x they are exactly the same but for y = -x , x is the opposite of y.

(3) Why do square root answers have a positive and negative result? Sample: sqrt{4} = +2 and -2. Why TWO answers?

Because when you square a number no matter if it is negative or positive you get a positive answer.

ex: x² = 25
___x = + or - √25
___x= + 5 or -5
because if you look at the original x² = 25
if you input -5 you get 25

(-5)² = 25...make sure when you type it into calculator you use the brackets.
25 = 25 because (-5)² is the same as -5 x -5 which is 25

same if you input 5 you also get 25
5² = 25
25 = 25

(4) What is the most basic difference between the words DOMAIN and RANGE?

The domain is all the x-values, and the range is all the y-values.

Answer 2

1) consider the x,y coordinate plane
in graphing a function only some points (in the plane) are representative of the function. y=f(x) is an equality, y does not mean the same thing as f(x). The EQUALITY is the set of points (x,y) such that y=f(x).

2) consider x=3 and the lines y=3 and y= -3
one line is above the axis, the other below

3) 2*2 = 4
(-2)*(-2) = 4
there exists more than one value for x such that x*x =4
all of these x are sqrt(4) for this question BOTH of these x=sqrt(4)

4) domain is the set of inputs (to a function), range is the set of outputs. Consider y=x^2 if the domain is the set of real number, the range is the positive reals and zero. Consider y=sqrt(x), if the domain is the reals, then the range is the union of the reals and the imaginary numbers. If the domain is the non-negative reals, the range is the non-negative reals

Answer 3

1) y equals to f(x) because f(x) means the function of x. u put a number for x and you would get y.

2)y=x if u grapht it will go up. if u graph y=-x the line would go down.

3) this is simple. square root basically means what 2 SAME factors get the product of 4. 2*2 = 4. 2 and 2 are the same factors. and -2 *-2 also equals 4. -2 and -2 are the same factors. so the answers for sqrt(4) = 2 and -2

4) domain is basically the input. if u have a function like 5x-3 the domain would be the number u put in for 5. the range or output would be the answer u get. lets take the function 5x-3 and substitute x for 3... 5*3-3 would be 12. so the range or output is 12.

hope that helps u a little

Answer 4

(1) They do not mean the same thing though they commonly show up that way.
Some day you may run into the case y = f(x,z).

(2) Think y=mx+b with b=0 so y=mx which gives you
y=(1)*x and y=(-1)*x which gives you two different slopes
that are perpendicular to each other.

(3) 2*2 = (-2)*(-2) = 4. So which one is right? They both are.

(4) The independent variable of a function (usually x) runs over each and every possible value in the domain and puts out some value
(usually y) in the range, which may or may not cover every
possible y, usually it doesn't. All x's for some y's or occassionly for all y's, but always all x's in the domain.

What is a function? It pays to have clear, clear idea.
It is worth seeing its relationship to other relationships.
Just search .

Answer 5

The coordinate system normally uses an x-axis and a y-axis.
We put in values of x and dtermine the value of y. Thus y is a function of x. But you can use whatever letters you like.
Y = f(theta). or y = f(t), or s = f(t).

The two lines are perpendicular to each other. One has a positive slope and the other a negative slope.

Because 2^2 = 4 and (-2)^2 = 4.

The domain indicates the values that x can assume.
The range is the values that y can assume over the legal x values.

Answer 6

1. because when not graphed you have to find the function output of the equation in terms of x
when graphed that function output is on the y cartesian plane so y = f(x)
2. they are perpendicular
3. because (-2)^2 and (2)^2 yield only 1 answer, 4
4. domain = x
range = y