QUESTION 1
The given function is
[tex]f(x)=7^x-4[/tex]
This function has a horizontal asymptote of [tex]y=-4[/tex].
To find the y-intercept, we put [tex]x=0[/tex] into the function to get;
[tex]f(0)=7^0-4[/tex]
[tex]f(0)=1-4[/tex]
[tex]f(0)=-3[/tex]
[tex]\boxed{horizontal\:asymptote:y=-4,y-intercept\:(0,-3)} \leftrightarrow \boxed{f(x)=7^x-4}[/tex]
QUESTION 2
The given function is
[tex]f(x)=3^{x+2}+4[/tex]
This function has a horizontal asymptote of [tex]y=4[/tex].
To find the y-intercept, we put [tex]x=0[/tex] into the function to get;
[tex]f(0)=3^{0+2}+4[/tex]
[tex]f(0)=9+4[/tex]
[tex]f(0)=13[/tex]
[tex]\boxed{horizontal\:asymptote:y=4,y-intercept\:(0,13)} \leftrightarrow \boxed{f(x)=3^{x+2}+4}[/tex]
QUESTION 3
The given function is
[tex]f(x)=9^{x+1}-4[/tex]
This function has a horizontal asymptote of [tex]y=-4[/tex].
To find the y-intercept, we put [tex]x=0[/tex] into the function to get;
[tex]f(0)=9^{0+1}-4[/tex]
[tex]f(0)=9-4[/tex]
[tex]f(0)=5[/tex]
[tex]\boxed{horizontal\:asymptote:y=-4,y-intercept\:(0,5)} \leftrightarrow \boxed{f(x)=9^{x+1}-4}[/tex]
QUESTION 4
The given function is
[tex]f(x)=2^x+4[/tex]
This function has a horizontal asymptote of [tex]y=4[/tex].
To find the y-intercept, we put [tex]x=0[/tex] into the function to get;
[tex]f(0)=2^0+4[/tex]
[tex]f(0)=1+4[/tex]
[tex]f(0)=5[/tex]
[tex]\boxed{horizontal\:asymptote:y=4,y-intercept\:(0,5)} \leftrightarrow \boxed{f(x)=2^x+4}[/tex]
