Question

The asymptote of the function f(x) = 3x + 1 – 2 is_________ . Its y-intercept is_____ .

Options for the first blank is
y= -2
y= -1
y= 1
y= 2
Options for the second is
(0,-2)
(0,-3)
(0,1)
(0,-1)

Answer 1

In first blank : y = - 2,

In second blank : ( 0, 1 )

Explanation:

Given function is,

`f(x)=3^(x+1)-2`

The horizontal asymptote of the function f(x),

`y=lim_(x\rightarrow \infty) f(x)`

`y=lim_(x\rightarrow \infty) 3^(x+1)-2`

`y=3^(\infty+1)-2`

`y=3^\infty - 2`

`y=0-2`

⇒ y = -2

First option is correct.

Also, the function has no vertical asymptote,

2. For finding the y-intercept, x = 0,

`f(0)=3^(0+1)-2=3-2=1`

Hence, the y-intercept = (0,1)

Third option is correct.