Question

The information below explains the transformations and translations of a logarithmic function. What is the equation for this function?
 Shift 4 units left
 Shift 3 units up
 Vertical Compress by 1/3
 Horizontal stretch by 3

Fill in the table below for the information of the function f(x) = log[-(x – 5)] + 4
Function
Log[-(x - 5)] + 4
Domain
Range
Interval of Increase/Decrease
Equation of Asymptote

Answer 1

The transformed function is y = 1/3(log(x/3 + 4)) + 1

How to transform the logarithmic function?

The parent logarithmic function is

y = log(x)

When shifted left by 4 units, we have:

y = log(x + 4)

When shifted up by 3 units, we have:

y = log(x + 4) + 3

When compressed vertically by 1/3, we have:

y = 1/3(log(x + 4) + 3)

This gives

y = 1/3(log(x + 4)) + 1

When stretched horizontally by 3, we have:

y = 1/3(log(x/3 + 4)) + 1

Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1

The transformation of function f(x)

We have:

f(x) = log[-(x – 5)] + 4

Set the radicand greater than 0

-(x - 5) > 0

Divide by -1

x - 5 < 0

Add 5 to both sides

x < 5 -- this represents the domain

A logarithmic function can output any real number.

So, the range is $-\infty < f(x) < \infty$

In the domain, we have:

x < 5

This means that the interval of decrease is $-\infty < x < 5$

Rewrite as an equation

x = 5 --- this represents the equation of asymptote

Read more about logarithmic functions at:

brainly.com/question/12708344

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