Decide whether the given relation is a function of x. (NO CREDIT WILL BE GIVEN WITHOUT AN EXPLANATION). Give the domain. y=-7/x-16
If you meant
y = -7/(x-16), then the domain is
any real number, x ≠ 16
and for every x you pick there is one and only one value of y , except x=16
so it is a function.
To determine if the given relation is a function of x, we need to check if there is a unique y-value for each x-value in the relation.
The given relation is y = -7/(x - 16).
To find the domain, we need to identify the values of x for which the relation is defined.
The relation is defined as long as the denominator (x - 16) is not equal to zero, as division by zero is undefined.
So, the domain of the relation is all real numbers except x = 16.
Now, let's check if the relation is a function.
To do this, we need to check if for each x-value in the domain, there is exactly one corresponding y-value.
Assuming x ≠ 16 (due to the domain restriction), we can calculate the y-values for different x-values.
Let's choose two values for x, say x = 10 and x = 20.
For x = 10:
y = -7/(10 - 16) = -7/(-6) = 7/6
For x = 20:
y = -7/(20 - 16) = -7/4
Thus, when x = 10, y = 7/6, and when x = 20, y = -7/4.
Since for each x-value there is a unique corresponding y-value, the relation is indeed a function of x.
In conclusion, the given relation y = -7/(x - 16) is a function of x with its domain being all real numbers except x = 16.