Question

The graph of an exponential function is given. Which of the following is the correct equation of the function? (2 points)

Answer 1

Option C

Explanation:

WE are given a graph of exponential function and asked to find out of four functions which function the graph represents.

We find that any function of the form

`y=a^x`

passes through (0,1) for all a

Hence we cannot distinguish any thing from the point

Let us consider when x=1

Then first function will have point as (1,2.4)

II funciton (1,0.31)

III function (1,0.45)

IV funciton (1,1.8)

From the graph given we find that the point of y is less than 1. Hence it can be either II or III

Consider x=-1

Then II function has point as (-1,3.225) and III function has point as (-1,2.222)

From the graph we find that the graph satsified only the point (-1,2.2222)

Hence OPtion III is right

Answer 2

`y=0.31^(x)`

B is correct

Explanation:

We are given exponential function graph. We need to choose correct equation of exponential function.

in graph we can see start from II quadrant and end in I quadrant.

It would be decay exponential function.

`y=ab^x`

b must be less than for given graph.

y-intercept of given graph is (0,1)

a=1, because y-intercept gives initial value of graph.

0<b<1

In the given option B and C whose b is less than 1.

Now, we take another point x=-1

For x=-1, the value of y of given graph between 3 and 4

Now we find value of y for x=-1

For option B:
`y=0.31^(-1)=3.2`

For option C:
`y=0.45^(-1)=2.2`

Hence, B is correct equation for given graph.