Which of the following statements are true regarding functions?
Check all that apply.
A. The horizontal line test may be used to determine whether a
function is one-to-one.
B. A sequence is a function whose domain is the set of rational
numbers.
C. A function is a relation in which multiple values of the input
variable are paired with at least one of the output variable.
D. The vertical line test may be used to determine whether a relation
is a function.

D

Step-by-step explanation:

The vertical line test, can be done with a pencil, and it's very simple. You run the object in a vertical position, horizontally across the graph, and if it hits two points on the same Y-Axis, your function is actually a relation, since functions are not allowed to have two coordinates on the same line.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

answer is 33

step-by-step explanation: