Question

+12 11 10 8 -5 4 3 2 4 5 6 7 8 Which one of the following equations could describe the graph above? O A. V=1.5(+2) - 3 V (0) +6 O B. O c. v= 3x - 1 O y D. Y=2*+6

Answer 1

The graph represents a decreasing function. We can see that because when x increases, the corresponding y decreases.

Also, the options show exponential functions, i.e., with the variable x in the exponent.

So, in order to solve this problem, we need to analyze the options to find which of them can describe the graph.

Notice that:

`\begin{gathered} \text{for a > 1, }a^x\text{ increases when x increases} \\ \\ \text{for 0 < a < 1, }a^x\text{ decreases when x increases} \end{gathered}`

Thus, for an exponential function to be an increasing function, a positive base, which has x as an exponent, needs to be less than 1.

And the only possible equation that satisfies that requirement is the one with base 1/2:

`y=\mleft((1)/(2)\mright)^x+6`

Notice that this equation indeed describes the graph, since for x = 0:

`y=\mleft((1)/(2)\mright)^0+6=1+6=7`

Therefore, option B is correct.