The exponential function $f(x)=e^{-x}+1$ crosses the $y$-axis at which of the following points?
$(0,1)$
$(1,0)$
$(2,0)$
$(0,2)$
Final Answer: \(\boxed{(0,2)}\)
Step 1 :The function $f(x)=e^{-x}+1$ crosses the y-axis when $x=0$. We need to substitute $x=0$ into the function to find the corresponding y-coordinate.
Step 2 :Substitute $x=0$ into the function: $f(0)=e^{-0}+1=1+1=2$
Step 3 :So, the function $f(x)=e^{-x}+1$ crosses the y-axis at the point $(0,2)$
Step 4 :Final Answer: \(\boxed{(0,2)}\)