In Check it Out, you should have discovered that an exponential function of the form y = abx has the following characteristics.

  • The a-value of the equation is equal to the y-intercept of the graph.

  • The a-value of the equation determines how slowly or how quickly the graph increases or decreases vertically.

 For example, if a = 4, then g(x) = 4(2)x increases four times as quickly in a vertical direction as the function f(x) = 2x.

On the other hand, h(x) = increases times as quickly in a vertical direction as the function f(x) = 2x.

  • The graph of the function increases from left to right if b > 1.

For p(x), an increasing exponential function, the graph extends from Quadrant II to Quadrant I.

The end behaviour can be described as follows. As the x-values decrease, the graph tends towards the x-axis. As the x-values increase, the graph tends towards positive infinity.

  • The graph of the function decreases from left to right if 0 < b < 1.

For m(x), a decreasing exponential function, the graph also extends from Quadrant II to Quadrant I.

The end behaviour can be described as follows. As the x-values decrease, the graph tends towards positive infinity. As the x-values increase, the graph tends towards the x-axis.

  • The shape of the graph is always concave up, or bowed up.