Math Homework. Do It Faster, Learn It Better.

Exponential Functions

The "basic" exponential function is the function

y = a x

where a is some positive constant.

For example, the graph of y = 2 x looks like this:

Note that:

1 ) The y -intercept is 1 (no matter what the value of a is).

2 ) The graph approaches the x -axis asymptotically as x goes to negative infinity (or as x goes to positive infinity, if 0 < a < 1 ).

3 ) The graph is always positive (never zero or negative).

The exponential function can be shifted k units upwards and h units to the right with the equation:

y = a x  −  h + k


Graph the equation.

y = 2 x  −  3 + 2

Start with the "basic" exponential graph y = 2 x . Then shift the graph three units to the right and two units up.