Question

Which function is graphed below?

Answer 1

The function whose graph is given is
`y=3 * 3^(-x)`

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:

`y= a * b^(-x)`

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;

`y= a * b^(-x)\\\Rightarrow 3= a * b^(-0)\\\Rightarrow 3= a`

Now when x=-1, we have y=9, so we get:

`y= a * b^(-x)\\\Rightarrow 9= 3 * b^(-1)\\\Rightarrow 3= b`

Thus, the function whose graph is given is
`y=3 * 3^(-x)`