Question

Which function is graphed below?
-

Answer 1

y=3 (1/3)x

Explanation:

On a graph, the closest graph you pictured is this answer

Answer 2

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

Explanation:

Step 1:

Check the y-intercept; in the graph, when x = 0, y = 3. Which equation satisfies this?

y =
`(1)/(3)`
`(3)^(x)` =
`(1)/(3)`
`(3)^(0)` =
`(1)/(3)` ❌

y =
`3 ((1)/(3) )^(x)` =
`3 ((1)/(3) )^(0)` = 3 ✅

y =
`((1)/(2) )^(x)` + 2 =
`((1)/(2) )^(0)` + 2 = 3 ✅

So the last two equations are possible.

Step 2:

Now check the y-value on the graph for any other x-value, whose corresponding y-value can be easily estimated from the graph.

For example, when x = 2, the y-value is between 0 and 1.

• 2nd equation: y =
`3 ((1)/(3) )^(x)` =
`3 ((1)/(3) )^(2)` = 0.333 ✅

• 3rd equation: y =
`((1)/(2) )^(x)` + 2 = y =
`((1)/(2) )^(2)` + 2 = 2. 25 ❌

∴ 2nd equation (y =
`3 ((1)/(3) )^(x)` ) is the one being represented by the graph.