Question

Please can someone help me with this math question ?

Answer 1

QUESTION 1

The given function is

$f(x)=7^x-4$

This function has a horizontal asymptote of $y=-4$.

To find the y-intercept, we put $x=0$ into the function to get;

$f(0)=7^0-4$

$f(0)=1-4$

$f(0)=-3$

$\boxed{horizontal\:asymptote:y=-4,y-intercept\:(0,-3)} \leftrightarrow \boxed{f(x)=7^x-4}$

QUESTION 2

The given function is

$f(x)=3^{x+2}+4$

This function has a horizontal asymptote of $y=4$.

To find the y-intercept, we put $x=0$ into the function to get;

$f(0)=3^{0+2}+4$

$f(0)=9+4$

$f(0)=13$

$\boxed{horizontal\:asymptote:y=4,y-intercept\:(0,13)} \leftrightarrow \boxed{f(x)=3^{x+2}+4}$

QUESTION 3

The given function is

$f(x)=9^{x+1}-4$

This function has a horizontal asymptote of $y=-4$.

To find the y-intercept, we put $x=0$ into the function to get;

$f(0)=9^{0+1}-4$

$f(0)=9-4$

$f(0)=5$

$\boxed{horizontal\:asymptote:y=-4,y-intercept\:(0,5)} \leftrightarrow \boxed{f(x)=9^{x+1}-4}$

QUESTION 4

The given function is

$f(x)=2^x+4$

This function has a horizontal asymptote of $y=4$.

To find the y-intercept, we put $x=0$ into the function to get;

$f(0)=2^0+4$

$f(0)=1+4$

$f(0)=5$

$\boxed{horizontal\:asymptote:y=4,y-intercept\:(0,5)} \leftrightarrow \boxed{f(x)=2^x+4}$