Domain & Range of Functions

[nycmath]

I am confused about f(x) versus f, especially after we have been taught that y = f(x).

For example, given f(x) = -3x + 7, find the domain and range of f.

Questions

1. Why can't we simply say find the domain and range of f(x)? Why simply f? Understand?

2. Why is the domain and range of linear functions always ALL REAL NUMBERS?

3. Can I say that the domain of functions is what can be plugged into the function without creating zero?

4. I need clarity using layman's terms. Is any of this correct?

(domain, range) = (x, y) leading to domain = x and range = y.

[Guest]

Hi its Bob.

1. [tex]f[/tex] is the function, the rule. [tex]f(x)[/tex] is its value at one [tex]x[/tex]. Domain and range belong to the whole function, so we say "of [tex]f[/tex]".

2. You can put any number into [tex]-3x + 7[/tex], and the line reaches every [tex]y[/tex] value. So both are all real numbers. The only exception is a flat line like [tex]f(x) = 5[/tex].

3. Not quite. Leave out any [tex]x[/tex] that makes you divide by zero or take the square root of a negative number.

4. Yes: the domain is the [tex]x[/tex] values you can put in, and the range is the [tex]y[/tex] values that come out.

[nycmath]

Hi its Bob.

1. [tex]f[/tex] is the function, the rule. [tex]f(x)[/tex] is its value at one [tex]x[/tex]. Domain and range belong to the whole function, so we say "of [tex]f[/tex]".

2. You can put any number into [tex]-3x + 7[/tex], and the line reaches every [tex]y[/tex] value. So both are all real numbers. The only exception is a flat line like [tex]f(x) = 5[/tex].

3. Not quite. Leave out any [tex]x[/tex] that makes you divide by zero or take the square root of a negative number.

4. Yes: the domain is the [tex]x[/tex] values you can put in, and the range is the [tex]y[/tex] values that come out.

Bob,

What is the domain and range of f(x) = 5?