YouTube Playlist: Logarithms and their Graphs

Recall that inverses are symmetric about the line

*y*=

*x*. For example,

**Step 1**: Find some points on the exponential

*f*(

*x*). The more points we plot the better the graph will look.

**Step 2**: Switch the

*x*and

*y*values to obtain points on the inverse.

**Step 3**: Determine the asymptote.

1.

**Graph the vertical asymptote**. All logarithmic functions of the form

*x*=

*h*.

2.

**Find the**. To find

*x*- and*y*-intercepts if they exist*x*-intercepts set

*y*=

*f*(

*x*) to zero and to find

*y*-intercepts set

*x*= 0.

3.

**Plot a few more points and graph it**.

**Graph the following logarithmic functions. State the domain and range.**

*y*= log(

*x*) then the first translation is a shift to the left 3 units

*y*= log(

*x*+3). Next we see a vertical shift up 2 units

*y*= log(

*x*+3)+2 .

*x*-axis as well as a shift to the left 3 units.

**YouTube Videos:**

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