range and domain?

Question

i don't get it...how do find the range and domain of quadratic equations, or logarithmic ones too-just for everything...

Answer 1

Range = like all the y values
Domain = all the x values

Example, quadratic.

y = 3x^2 + 4x + 3

As y approaches infinity
x approaches infinity

So Domain is -infinity < x > +infinity or x is an element of real numbers.

Find the turning point for the range

-b/2a = -4/6 for the x
and f(-b/2a) = 3* -4/6 ^ 2 - 16/6 + 3 = 1 + 2/3

So the range is

y > 1+2/3

Logarithmic example

1/x

The is an asymtote at x = 0 so

Domain = an element of real numbers
Range = an element of the real number where x =/ to 0

Answer 2

To find the domain of quadratic functions, usually the best thing to do is to put them in the form y = a(x - h)^2 + k.

If your quadratic function is in the above form, it follows the vertex will be at (h, k), and k is either going to be your highest point or lowest point.

If "a", the constant in front of (x - h) is a positive number, then (h, k) will be a minimum, and your range will be [k, infinity) OR

{x | x >= k, for all real numbers x}.

If "a" is negative, (h,k) will be a maximum, and your range will be (-infinity, k].

The domain of quadratic equations is always all real numbers.

Answer 3

Solve for y: (x-a)^2+ (y-b)^2 = p.
For any possible values of x, this becomes the domain.
It follows that the range is all the values of y when you plug in x.

To find the domain, find all possible values for x.
To find the range, find the possible greatest upper bound and the least lower bound for y.