Use a graph to determine if the exponential function g(x)= -6*5^x is positive or negative and increasing or decreasing.

Question

a. positive, increasing
b. positive, decreasing
c. negative, increasing
d. negative, decreasing

Answer 1

To determine if the exponential function is positive or negative, we need to examine the values of the function for different values of x. The function is given by g(x) = -6 * 5^x.

Let's consider a few values of x:

For x = 0: g(0) = -6 * 5^0 = -6 * 1 = -6
For x = 1: g(1) = -6 * 5^1 = -6 * 5 = -30
For x = 2: g(2) = -6 * 5^2 = -6 * 25 = -150
For x = 3: g(3) = -6 * 5^3 = -6 * 125 = -750

From these calculations, we can see that when x increases, the values of g(x) become more negative. Therefore, the exponential function g(x) = -6 * 5^x is negative.

To determine if the exponential function is increasing or decreasing, we can look at the slope of the graph. The slope of an exponential function increases as the base of the exponent increases.

In this case, the base of the exponent is 5. As the base is greater than 1, the exponential function is increasing.

Therefore, the exponential function g(x) = -6 * 5^x is negative and increasing.

The correct answer is c. negative, increasing.