Final answer:
To graph the exponential function g(x) = 3^x - 3, plot the y-intercept and calculate g(x) for a range of x values. The graph approaches y = -3 as an asymptote for negative x and rises exponentially as x increases.
Step-by-step explanation:
The question pertains to graphing an exponential function, specifically g(x) = 3x - 3. In graphing this function, start by plotting the y-intercept, which is the value of g(x) when x = 0. In this case, g(0) = 30 - 3 = 1 - 3 = -2, so the y-intercept is -2. As x increases, the value of 3x grows exponentially, while the -3 translates the graph vertically downwards by 3 units.
For each table value of x, calculate g(x) = 3x - 3 and plot the points on a graph with labeled x- and y-axes. Connect these points smoothly since exponential graphs are continuous.
You will notice that as x approaches negative infinity, the graph approaches the line y = -3 asymptotically, since anything raised to a negative power yields a fraction and subtracting 3 will always result in values close to -3.
In this context, the graph does not represent a straight line with a consistent slope, unlike the example given; exponential functions have a variable rate of change.
However, understanding the nature of exponential growth and decay is crucial. The exponential growth rate here is determined by the base of the exponent, which is 3 in g(x) = 3x - 3.