Question

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

Answer 1

Asymptote is y = -1

y-intercept is (0, -1)

Answer 2

Answer:

In first blank : y = - 2,

In second blank : ( 0, 1 )

Step-by-step 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.