Maged Saeed said:Yeah I got it now ..
You mean that y is greater than zero so the range is from zero to infinity
x is all real number !
right ?
MarkFL said:$y$ and be any non-negative real number, including zero. Squaring, we obtain:
\(\displaystyle y^2=x^2+y^2\)
What does this tell you about $x$?
A domain is the set of all possible input values for a function, while a range is the set of all possible output values for a function.
To find the domain and range of a function, we need to look at the restrictions on the input values and the possible output values. For a square root function like y=√(x^2+y^2), the radicand (the expression under the square root) must be greater than or equal to 0, so the domain is all real numbers. The range depends on the value of y, but it will always be greater than or equal to 0 since the square root of a non-negative number is always non-negative.
Yes, the domain and range of a function can be infinite as long as there are no restrictions on the input or output values. In the case of y=√(x^2+y^2), the domain and range are both infinite since there are no restrictions on the values of x and y.
To graph a function and determine its domain and range, we can plot several points and connect them to create a curve. The domain and range can then be determined by looking at the x and y values of the plot. For y=√(x^2+y^2), we can plot points with different values of x and y to see that the curve extends infinitely in all directions, indicating an infinite domain and range.
Finding the domain and range of a function is important because it helps us understand the behavior of the function. It also allows us to determine the set of valid input and output values, which can be useful in solving equations and making predictions about the function. In some cases, the domain and range can also provide insights into the symmetry and shape of a function.