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They intercept in two points.
The graph y=x^2 is very basic so I suppose you know how it looks like.
It's like a U and starts from the origin (0,0)
The graph y=cosx is similar to y=x^2 but in a different way.
y=cosx doesn't pass from (0,0) it passes from (0,1) and then to (-1,0) and (1,0).
Basically, it goes like this..
~
If you know how the two graphs look like then you can understand why they intercept only two times.
The graph y=x^2 is very basic so I suppose you know how it looks like.
It's like a U and starts from the origin (0,0)
The graph y=cosx is similar to y=x^2 but in a different way.
y=cosx doesn't pass from (0,0) it passes from (0,1) and then to (-1,0) and (1,0).
Basically, it goes like this..
~
If you know how the two graphs look like then you can understand why they intercept only two times.
The transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>How to transform the logarithmic function?</h3>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
<h3>The transformation of function f(x)</h3>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
In the domain, we have:
x < 5
This means that the interval of decrease is
Rewrite as an equation
x = 5 --- this represents the equation of asymptote
Read more about logarithmic functions at:
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