Answer:
First option (top left)
Step-by-step explanation:
Since the coefficient of this equation, [tex]2(3)^{x}[/tex], is 2, when x is 0, then y must be 2. The graph must have a y-intercept of 2. You can find this by plugging this in.
I cannot see the fourth graph, but the second graph does not have a y-intercept of 2, therefore it can immedeately be ruled out.
Then we plug in the coordinates they give.
It just so happens that the first one, [tex]2(3)^1[/tex] is indeed equal to 6.
We can check that this is right by disproving the third one (top right).
[tex]2(3)^2=18[/tex], not 8, therefore our third answer choice is false.
The fourth one is definetly wrong because the y-value at x=2 (as we have already calculated) is 18, not 12.
Therefore, our first answer, the one on the top left, is correct.
note: for this problem you did not even need to find the y-intercepts. Plugging in the coordinates would be fine by its own (the second answer choice is already wrong just because of the coordinates since 9≠6(found in answer choice 1)). However, having the y-intercept handy will be very helpful if there is more than one answer choice with correct coordinates.
