Which of the following is true for the relation f(x) = x^2 + 8? only the inverse is a function. only the equation is a function. neither the equation nor its inverse is a function. both the equation and its inverse are functions.

both the equation listed above and the inverse are functions.

we know that the equation above is a function because firstly, it is a quadratic, which is a type of function. we also know it is a function because there is only 1 output for all of the inputs we can use, or to put it more simply, no matter what x we put in, only one y value comes out.

to find if the inverse is a function, we first have to find the inverse. you can find the inverse to any function by switching the x and f(x) values. after that, solve for the new f(x) value. the result will be the inverse function. the step-by-step process for this one is done below for you.

f(x) = x^2 + 8 > switch the x and f(x)

x = f(x)^2 + 8 > subtract 8 from both sides

x - 8 = f(x)^2 > take the square root of both sides

f(x) =

and this is also a function because we only get one output for every input. therefore, both are functions.

idk but i found this "the graph of y = f(x-2) is the graph of y = f(x) translated two units rightward.  

so, since the point (9,2) lies on the graph of y = f(x), the point (11,2) lies on the graph of y = f(x-2)."

step-by-step explanation:

link is

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.