Question

Which function is graphed below?

Answer 1

Answer:
`y = 3((1)/(3) )^x`

Explanation:

First off we can observe that this graph shows exponential decay since the y-value decreases exponentially as the x-value increases. Notice that the y-values for options
`y = (1)/(3) (3)^x` and
`y=(2)^x-1` will increase as x increases because the bases (3 and 2 respectively) are greater than 1.

That leaves options
`y = 3((1)/(3))^x` and
`y = ((1)/(2))^x + 2`. Let's the point at which x = 1 and y = 1. When we plug in the given x-value, it should correspond with the y-value.

`y = 3((1)/(3))^1\\y = (3)/(3)\\y = 1`

`y = ((1)/(2))^1+2\\y = (1)/(2) +2\\y = (5)/(2) \\eq 1`

By plugging in the values we can see that the equation
`y = ((1)/(2))^x + 2` does not equal 1 when x = 1. The equation
`y = 3((1)/(3))^x` does meet this criterion, therefore it is the answer.