Answer:
In first blank : y = - 2,
In second blank : ( 0, 1 )
Step-by-step explanation:
Given function is,
[tex]f(x)=3^{x+1}-2[/tex]
The horizontal asymptote of the function f(x),
[tex]y=lim_{x\rightarrow \infty} f(x)[/tex]
[tex]y=lim_{x\rightarrow \infty} 3^{x+1}-2[/tex]
[tex]y=3^{\infty+1}-2[/tex]
[tex]y=3^\infty - 2[/tex]
[tex]y=0-2[/tex]
⇒ y = -2
First option is correct.
Also, the function has no vertical asymptote,
2. For finding the y-intercept, x = 0,
[tex]f(0)=3^{0+1}-2=3-2=1[/tex]
Hence, the y-intercept = (0,1)
Third option is correct.
