The exponential function f, whose graph is given below, can be written as
1 answer:
Answer:
f(x) = 2·3^x
Step-by-step explanation:
We have the general equation of exponential functions as
y= a*b^x
We are given that the point (0,2) is on the graph so
when x= 0, y= 2
If we substitute in the general equation we see that
2 = a*b^0, any number to the power 0 is 1
2 = a
We were also given that point (1, 6 ) is on the graph;
If we substitute in our new found equation we see that
y=2·b^x
6 = 2·b^1 , any number to the power 1 is itself and
divide both sides by 2
3 = b
f(x) = 2·3^x
You might be interested in
This is a downward facing parabola, so its range comes in the form
where m is the y coordinate of the vertex of the parabola.
We can find the x coordinate of the vertex using
And if we plug -1 in the equation we get the y coordinate of the vertex:
So, the range is the interval