Question

5 select the correct answer from each drop - down menu. the asymptote of the function f(x)=3^{x + 1}-2 is its y - intercept is y = - 2 y = - 1 y = 1 y = 2 reset next

Explanation:

Step1: Find the horizontal - asymptote

For an exponential function of the form $y = a\cdot b^{x + h}+k$, the horizontal asymptote is $y = k$. In the function $r(x)=3^{x + 1}-2$, $a = 3$, $b = 3$, $h = 1$, and $k=-2$. So the horizontal asymptote is $y=-2$.

Step2: Find the y - intercept

The y - intercept is found by setting $x = 0$. Substitute $x = 0$ into $r(x)=3^{x + 1}-2$. Then $r(0)=3^{0 + 1}-2=3 - 2=1$.

Answer:

The asymptote of the function $r(x)=3^{x + 1}-2$ is $y=-2$. Its $y$-intercept is $1$.