Logarithmic Functions and Properties

$$y=\frac{1}{12}$$

$$x=12$$

$$x=-12$$

$$y=-12$$

$$y=\frac{1}{5}$$  

$$x=5$$

$$y=5$$

$$y=-1$$

$$x=-1$$

$$x=1$$

$$y=1$$

$$\left(-\infty,\infty\right)$$  

$$\left(\infty,-\infty\right)$$  

Cannot determine from the given information.

$$\left(\infty,3\right)$$  

$$\left(3,\infty\right)$$  

Cannot determine from the given information.

$$\left(\infty,1\right)$$  

$$\left(-1,\infty\right)$$  

Cannot determine from the given information.

yellow: y=0

green: x=0

yellow: y=1

green: x=1

yellow: y=-1

green: x=-1

yellow: y=-1

green: x=1

Domain:

Domain:
$$\left(-\infty,\infty\right)$$

Range: $$\left(-1,\infty\right)$$

Range: $$\left(-\infty,\infty\right)$$

$$as\ \left[x\rightarrow0\right],\ \left[y\rightarrow-\infty\right];\ as\ \left[x\rightarrow\infty\right],\ \left[y\rightarrow\infty\right]$$

$$as\ \left[x\rightarrow0,\ y\rightarrow0\right];\ and\ as\ \left[x\rightarrow\infty,\ y\rightarrow\infty\right]$$