how would you find the domain and range?

Question

i have no problem to use as an example

Answer 1

domain would be the valid numbers for x (the input).
range would be the valid numbers for y (the output).

Take the function:
y = 5x + 7

Here the domain would all real numbers. You can pick x as small as you like, or as big as you like with no restrictions.

Similarly, the value of y will end up being valid with any input, so the range is all real numbers without restrictions.

Let's take a different example.
y = 1/x

Here we have a problem if x = 0 because 1/0 is undefined. So the range here would be all real numbers, except x = 0.

As for the values of y, try solving the equation for x:
x = 1/y

Ah, we now see that we will never have y = 0 in the output, but all other real numbers are allowed. So the range is all real numbers except y = 0.

Here's one last example:
y = sqrt(x).

The domain is all *non-negative* real numbers. If you a negative number for x you can't take the square root.

And the output (range) is all real numbers. (Well, technically it depends on whether you mean the positive square root, or all roots.)

Anyway, do you get it now?

Answer 2

f(x)=x^2+1
Domain is all the possible values for which the function can be defined.
Here, the domain is the real line(i.e. any number). Given any number, say 2 or -2, you can find f(x)
f(2)=2^2+1=5
f(-2)=(-2)^2+1=5
Range is all the values the function will result in.
Here, the range is all positive numbers and 0.
Note that f(x) cannot be negative. If x=-1
f(x)=(-1)^2+1=2

consider f(x)=1/x
Except 0, f(x) has a value.
The domain is all numbers except 0.
The range is all numbers except 0. f(x) will not result in 0 for any x.

Answer 3

Domain of a Function:

For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly.

Range of a Function:

The range of f is the set of all values that the function takes when x takes values in the domain.

Answer 4

domain is the x values and range is the y values