Graph the function y=3(5)x. What is the y-value if x=−6?
To graph the function y=3(5)x, we start by plotting a few points. We choose different x-values and substitute them into the equation to find the corresponding y-values.
When x = -2, y = 3(5)^(-2) = 3/25 ≈ 0.12
When x = -1, y = 3(5)^(-1) = 3/5 = 0.6
When x = 0, y = 3(5)^0 = 3(1) = 3
When x = 1, y = 3(5)^1 = 3(5) = 15
When x = 2, y = 3(5)^2 = 3(25) = 75
Plotting these points and drawing a curve that passes through them, we get the graph of the function as shown below:
graph{
3*(5)^x [x range=-6:6, y range=-500:500]
}
Now, to find the y-value when x = -6, we substitute x = -6 into the equation:
y = 3(5)^(-6)
y = 3/5^6
y = 3/15625 ≈ 0.000192
Therefore, the y-value when x = -6 is approximately 0.000192.