Question

Graph the exponential function y=0.5(6)x. Identify the y-intercept.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To graph the exponential function y=0.5(6)^x, we can create a table of values and plot the points.

Let's substitute some x-values and calculate the corresponding y-values:

For x = -2: y = 0.5(6)^(-2) = 0.5/36 = 1/72
For x = -1: y = 0.5(6)^(-1) = 0.5/6 = 1/12
For x = 0: y = 0.5(6)^0 = 0.5(1) = 0.5
For x = 1: y = 0.5(6)^1 = 0.5(6) = 3
For x = 2: y = 0.5(6)^2 = 0.5(36) = 18

Using these points, we can plot the graph:

x | y
-2 | 1/72
-1 | 1/12
0 | 0.5
1 | 3
2 | 18

Now let's plot these points on a graph:

The y-intercept is a point on the graph where x = 0. From the table, we can see that when x = 0, y = 0.5. Therefore, the y-intercept is (0, 0.5).

Here is the graph of the exponential function y=0.5(6)^x with the y-intercept marked:

(Function graph goes from (1/72 lightly beside the curve), (1/12), (0.5), 3, 18 with the y-intercept point at (0, 0.5) slightly labelled).