Answer:
The function whose graph is given is [tex]y=3 * 3^{-x}[/tex]
Step-by-step explanation:
Now, to find the equation of the function, when the graph is already given in the question, we can use the various coordinates points. The x-intercept and the y-intercept can be used first.
So here the graph is of the form:
[tex]y= a * b^{-x}[/tex]
Now to find the value of the arbitrary constants a and b , we will use the y -intercept (0,3) and point (-1,9) where the curve is passing from.
Now when x=0, we have y= 3, which means that;
[tex]y= a * b^{-x}\\\Rightarrow 3= a * b^{-0}\\\Rightarrow 3= a[/tex]
Now when x=-1, we have y=9, so we get:
[tex]y= a * b^{-x}\\\Rightarrow 9= 3 * b^{-1}\\\Rightarrow 3= b[/tex]
Thus, the function whose graph is given is [tex]y=3 * 3^{-x}[/tex]
