How do I find the domain of the funcition algebraically and support my answer graphically?
f(x) = sqrt(x2) + (4)
sqrt (x^2) = x, so I assume you meant to write
f(x) = sqrt(x^2 +4)
The quantity in ( ) is always positive, so there is always a real square root, regardless of the value of x.
The domain is all positive and negative real numbers.
please help me with this problem? I have the answer but I need to know how to do it.
Use the point on the line and the slope of the line to find three additional points through which the line passes
point slope
((7,-2) m= 1/2
To find the domain of a function algebraically, we need to consider the values of x for which the function is defined. In this case, we have the function:
f(x) = √(x^2) + 4
The square root of a number is defined for non-negative real numbers, so we need to ensure that the expression inside the square root (x^2) is non-negative. Since x^2 is always non-negative for any real value of x, we don't have any constraints on the domain based on the square root.
However, we still need to consider any other restrictions on the domain. In this case, there are no other terms in the function that could limit the domain. Therefore, the domain of f(x) is all real numbers (-∞, +∞).
To support our answer graphically, we can plot the graph of the function. This will show that the function is defined for all real values of x:
First, let's plot the graph of f(x) = √(x^2):
The graph of the square root function (without the + 4) is a graph of a semicircle, where the function is defined for x ≥ 0.
Next, let's add the constant term + 4 to the graph. This will shift the entire graph upward by 4 units:
Now, we can see that the graph of f(x) = √(x^2) + 4 is defined for all real values of x since it is a shifted semicircle that is continuous for all x.
Thus, both algebraically and graphically, we can conclude that the domain of f(x) = √(x^2) + 4 is (-∞, +∞).