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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 .

Respuesta :

sam4040

Answer:

As [tex]x[/tex] increases without bound, [tex]f(x)[/tex] increases without bound.

Step-by-step explanation:

[tex]Given\ f(x)=413x+3\\f(1)=413+3=416\\f(2)=413\times 2+3=829\\f(3)=413\times 3+3=1242\\.\\.\\.\\[/tex]

Hence with the increasing value of [tex]x[/tex], [tex]f(x)[/tex] increases.

[tex]x[/tex] can be any value between [tex]-\infty[/tex] to [tex]\infty[/tex] and [tex]f(x)[/tex] can have any value between [tex]-\infty[/tex] to [tex]\infty[/tex].

Hence as [tex]x[/tex] increases without bound, [tex]f(x)[/tex] increases without bound.

This can be seen from the graph attached(with the increasing value of [tex]x[/tex], [tex]f(x)[/tex] increases.

Ver imagen sam4040

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