Training Camp (cont 2)

In summary, the logarithmic functions y = a log x and y = a ln x both have the following characteristics.

• The graph has an x-intercept at 1.

• The graph has no y-intercept. The graph approaches but never touches the y-axis.

• The graph of the function increases from left to right if a > 0.

  For f(x), an increasing logarithmic function, the graph extends from Quadrant IV to Quadrant I. The end behaviour can be described as follows. As the x-values decrease, the graph tends towards the y-axis. As the x-values increase, the graph tends towards positive infinity.

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

  For g(x), a decreasing logarithmic function, the graph extends from Quadrant I to Quadrant IV. The end behaviour can be described as follows. As the x-values decrease, the graph tends towards the y-axis. As the x-values increase, the graph tends towards negative infinity.

Regardless of whether the logarithmic functions shown above are increasing or decreasing, they will never have an x-value less than or equal to zero. Because of this, they will never cross the y-axis; therefore, they have no y-intercepts. Based on this information, you can specify the domain and range as follows.