Key Features of Exponential functions

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where $$a$$ is a constant, $$b$$ is a positive real number, and @@b eq 1@@.

The base of an exponential function determines the rate of growth or decay. If $$b > 1$$ , the function represents exponential growth; if $$0 < b < 1$$ , it represents exponential decay.

The y-intercept of an exponential function $$f(x) = a \times b^x$$ is the value of $$f(0)$$ , which equals $$a$$ .

The horizontal asymptote of an exponential function is the line $$y = 0$$ , which the graph approaches but never touches as $$x$$ approaches negative infinity.

An exponential function is increasing if the base $$b > 1$$ and decreasing if $$0 < b < 1$$ .

The initial value (y-intercept) is 6, which is the value of $$f(0)$$ .

The equation of the asymptote is $$y = 0$$ .

Having a y-intercept at a certain point means that the graph of the function crosses the y-axis at that value when $$x = 0$$ .

The general form of an exponential decay function is $$f(x) = a \times b^x$$ , where $$0 < b < 1$$ .

You can identify the y-intercept by evaluating the function at $$x = 0$$ , which gives you $$f(0) = a$$ .