Determine the domain and range of
y= (radical) x-4
y= (radical) x^2-4
plz help me step by step. I just need to refreash my math, but i forgot how to find it
do you mean
y = sqrt(x-4) ???
if so the right side is real only for x>/= +4 so domain is all x >/= +4 and range is all positive y
If the second one is
y = sqrt (x^2-4)
then (x^2-4) is real only for |x|>/=2
so domain is all x </- -2 and all x>/=+2
and again y is always +
how do u figures out the doamin and range???
To determine the domain and range of a function, you need to consider the restrictions on the input (x-values) and the resulting output (y-values). Let's break down the process step by step for each function:
1. y = √(x - 4)
Domain:
The domain represents the set of all possible values that the input (x) can take. In the case of a square root function, the value inside the square root (√) must be non-negative, as we cannot take the square root of a negative number. Therefore, to find the domain, set the expression inside the square root greater than or equal to zero and solve for x:
x - 4 ≥ 0
x ≥ 4
So, the domain for this function is all real values greater than or equal to 4.
Range:
The range represents the set of all possible values that the output (y) can take. In this case, since the square root function always returns a non-negative value (or zero), the range will be all real values greater than or equal to zero. Therefore, the range is y ≥ 0.
2. y = √(x^2 - 4)
Domain:
Similar to the previous example, we need to find the values of x for which the expression inside the square root (√) is greater than or equal to zero:
x^2 - 4 ≥ 0
This is a quadratic equation, so let's solve it:
(x - 2)(x + 2) ≥ 0
Now, we can determine the sign of the expression by examining the signs of the factors:
For (x - 2) ≥ 0:
x ≥ 2
For (x + 2) ≥ 0:
x ≤ -2
Therefore, the domain for this function is all real values such that x ≤ -2 or x ≥ 2.
Range:
For positive values of x, the square root (√) of x^2 - 4 will be non-negative or zero. Therefore, the range of this function is y ≥ 0.
I hope this clarifies the process of finding the domain and range for these functions. Let me know if you have any further questions!