What is the $$ y $$-intercept of $$ f(x)=3+3^{x-2} $$ ? $$ \square $$ (Type an integer or a simplified fraction

Question

UpStudy AI · Accepted Answer

1. We find the $$ y $$-intercept by evaluating the function at $$ x=0 $$.

2. Substitute $$ x = 0 $$ into the function:
   $$
   f(0) = 3 + 3^{0-2} = 3 + 3^{-2}
   $$

3. Simplify $$ 3^{-2} $$:
   $$
   3^{-2} = \frac{1}{3^2} = \frac{1}{9}
   $$

4. Add the terms:
   $$
   f(0) = 3 + \frac{1}{9} = \frac{27}{9} + \frac{1}{9} = \frac{28}{9}
   $$

Thus, the $$ y $$-intercept is $$\frac{28}{9}$$.
The $$ y $$-intercept is $$\frac{28}{9}$$.

What is the -intercept of ?
(Type an integer or a simplified fraction