Graphing Logarithmic Functions

To draw the graph of a logarithmic function, we can follow a three-step process.

Let's do it!

Looking at the given function, we can see that the base is $b = \frac{1}{4} .$ $f (x) = lo g_{\frac{1}{4}} (x)$

Using the base, we can identify three points on the graph of a logarithmic function.

(1, 0), (b, 1), and (\frac{1}{b}, - 1)

Since we know that

b = \frac{1}{4},

we already have that

(b, 1)

=

(\frac{1}{4}, 1) .

Let's now calculate

(\frac{1}{b}, - 1) .

(\frac{1}{b}, - 1)

b = \frac{1}{4}

(\frac{1}{1 / 4}, - 1)

Simplify

\frac{a}{b / c} = \frac{a \cdot c}{b}

(\frac{1 ( 4 )}{1}, - 1)

a \cdot 1 = a

(\frac{4}{1}, - 1)

CalcQuotCalculate quotient

(4, - 1)

Finally, we will plot the three points and connect them with a smooth curve.

Useful Theory

The graph depends on the value of the base $b .$ If $b > 1,$ the curve increases. If $0 < b < 1,$ the curve decreases. Try it below!

b > 1

0 < b < 1

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Graphing Logarithmic Functions 1.12 - Solution