Question

In: Advanced Math

Use f(x) = log3 (x) as the parent function. For the following exercises, write a logarithmic equation corresponding to the ...

For the following exercises, write a logarithmic equation corresponding to the graph shown.

Use f(x) = log3 (x) as the parent function.

Expert Solution

Refer to the graph shown in the exercise.

From the graph the vertical asymptote is x = -4 and has been vertically reflected.

The equation will be in the form;

y = blog3(x + 4) + k

It appears the graph passes through the points (-3, 0) and (-1, -3) substitute (-3, 0) as follows:

0 = alog3(-3 + 4) + k

0 = alog3(1) + k

0 = 0 + k

k = 0

Now substitute (-1, -3) as follows:

-3 = alog3(-1 + 4) + 0

-3 = alog3(3)

a = -3

Here the reflection is along y-axis.

Thus the equation of the function is -3log3(x + 4).

Now check the equation by graphing the function as shown below:

Here the reflection is along y-axis.

Thus the equation of the function is -3log3(x + 4).

Junaid answered 1 year ago

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