Question

Which of the following describes the graph of g(x) = –ln(x – 4)?

a) Parabola opening upward
b) Exponential decay
c) Hyperbola
d) Logarithmic decay

Answer 1

The graph of g(x) = –ln(x – 4) represents logarithmic decay. By plotting points and connecting them, we can see that the graph approaches the x-axis as x increases.

Step-by-step explanation:

The graph of g(x) = –ln(x – 4) represents logarithmic decay. A logarithmic function is a type of non-linear function where the output varies exponentially with respect to the input. In this case, the natural logarithm function is being applied to the expression (x – 4) to produce the output value.

To better understand how this function behaves, let's look at an example:

If we substitute different values for x into the equation and compute the resulting y values, we can plot these points on a graph. For example, when x = 5, the equation becomes:

g(5) = –ln(5 – 4) = –ln(1) = 0

So, the point (5,0) belongs to the graph of g(x). By finding more points and connecting them, we can see that the graph of g(x) approaches the x-axis as x increases, which is characteristic of logarithmic decay.