Question

Which answers describe the end behaviors of the function modeled by the graph?

f(x)=413x+3 ,

Select each correct answer.


As x increases without bound, f(x) increases without bound.

As x increases without bound, f(x) decreases without bound.

As x increases without bound, f(x) approaches the line y=3 .

As x decreases without bound, f(x) approaches the line y=3 .

Answer 1

As
`x` increases without bound,
`f(x)` increases without bound.

Explanation:

`Given\ f(x)=413x+3\\f(1)=413+3=416\\f(2)=413* 2+3=829\\f(3)=413* 3+3=1242\\.\\.\\.\\`

Hence with the increasing value of
`x`,
`f(x)` increases.

`x` can be any value between
`-\infty` to
`\infty` and
`f(x)` can have any value between
`-\infty` to
`\infty`.

Hence as
`x` increases without bound,
`f(x)` increases without bound.

This can be seen from the graph attached(with the increasing value of
`x`,
`f(x)` increases.