What is the domain and range of this function: f(x)= x^2+11 ?

Answer 1

Lots of my students get domain and range confused. There is a simple way to understand what you are talking about when it comes to these. First, graph the function. This is a simple graph that looks like a giant "U" that is spreading further and further apart at the top, and the bottom of the "U" is centered on 11 of the y axis. Now, you can think of the domain as everywhere the graph will touch an x value, and the range is everywhere the graph will touch a y value. X values go from left to right, and Y values go up and down. It is important to understand that the graph of x^2 will never stop spreading at the top. With this information, we can see that the graph will eventually touch every x value from negative infinity on the left to positive infinity on the right. So that is your domain. Also looking at the graph, it is easy to see that the graph will keep going up forever, but the bottom will never go below the 11. This gives us a range from 11 (on the bottom) to positive infinity (on the top). Since the graph goes through the 11 on the y axis, we say that 11 is "included" in the range. This is shown with a bracket "[" instead of a parenthesis "(". It looks like this...
domain: (-infinity, infinity)
range: [11, infinity)
You don't put brackets around infinity because infinity cannot be contained.
I hope this helps you understand.

Answer 2

f(x) = x^2 + 11

The domain of all polynomials (including quadratics) is all real numbers.

To get the range of a quadratic function in the form

f(x) = a(x - h) + k

If a is positive, then the range will be [k, infinity). In set notation, this is
"the set of all y such that y >= 11"

{y | y >= 11}

If a is negative, then the range will be (-infinity, k], or, in set notation,
"The set of all y such that y <= 11"

{y | y <= 11}

In our case, f(x) = x^2 + 11, which is the same as

f(x) = 1(x - 0)^2 + 11

Which means our range is [11, infinity).

Answer 3

If you factorise the equation, you will get 2 answers and then use the obtained answer to get the value of x. For example, you got these two:
(x-2)=0
So, x = 2.
Then, use the obtained value to find the value of f(x) like this:
f(x) = 2^2 + 11
f(x) = 15

So, the domain is 2 and the range is 15 in my example. Work out the values yourself. ^.^

domain is x and range is y in another sense.

Answer 4

D: x = all real numbers
R: Obviously, x^2 must be bigger than or equal to zero. So the range y must be bigger than or equal to zero plus 11.
Therefore, the range y must be bigger than or equal to 11.

Answer 5

domain is real number
range f(x)>=11