Answer:
[tex]y=e^x+3[/tex]
Step-by-step explanation:
By inspection, we can see that the curve crosses the y-axis at (0, 4)
Therefore, when x = 0, y = 4
Inputting x = 0 into the equations:
[tex]y=e^{x-3} \implies y=e^{-3}[/tex]
[tex]y=e^x+3 \implies y=e^0+3=1+3=4[/tex]
[tex]y=e^{x+3} \implies y=e^4[/tex]
[tex]y=e^{x-3}+3^3=e^{-3}+27[/tex]
Therefore, the only equation that gives y = 4 when x = 0 is [tex]y=e^x+3[/tex]
