Why is (8+5)/25 irrational
2 answers:
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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
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The Domain is (-∞, -2) U (-2, 2) U (2, ∞) and Range is (-∞, -2) U [-1, ∞) and x-intercept = (-1.5, 0), (1.5, 0) and y-intercept = (0, -1).
<h3>What is a conic section?</h3>It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (circle is a special of type of ellipse).
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
From the graph:
a) The domain: all values of x
The range: all values of y
Except: Values at asymptotes are excluded.
Domain = (-∞, -2) U (-2, 2) U (2, ∞)
Range = (-∞, -2) U [-1, ∞)
b)
x-intercept = (-1.5, 0), (1.5, 0)
y-intercept = (0, -1)
c) Horiznotal asymptotes: y = -2
d)Vetical asymptotes: x = -2, x = 2
e) Oblique asymptotes: There is no oblique asymptotes
Thus, the Domain is (-∞, -2) U (-2, 2) U (2, ∞) and Range is (-∞, -2) U [-1, ∞) and x-intercept = (-1.5, 0), (1.5, 0) and y-intercept = (0, -1).
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