Comparing Functions

The applet below contains linear, quadratic and exponential functions. Each function is color-coded so its graph is the same color as its description & equation listed on the right. Of all these listed functions, which one will eventually "beat all the others", so to speak, with respect to increasing at the fastest rate? Explain your reasoning.

Linear, quadratic and exponential functions

What are the y-intercepts for each function?

The y-intercept for f(x) is _____________. The y-intercept for g(x) is _____________. The y-intercept for h(x) is _____________.

What do you notice about the graph of each function?

The linear function _______________________________________________________________________________________. The quadratic function ___________________________________________________________________________________. The exponential function _________________________________________________________________________________.