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Home Q & A Board Science-Related Homework Help Mathematics Pre-calculus and Functions
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marinejas marinejas
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3 years ago
(continued) results from each of the following pairs of transformations:
a) vertical stretch by a factor of 5, vertical translation 3 units up.
b) reflection in the x-axis, horizontal compression by a factor of 1/3.
c) horizontal translation 4 units left, vertical translation 3 units down
d) reflection in the x-axis, horizontal translation 4 units right
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bio_manbio_man
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#1
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3 years ago
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marinejas Author
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#2
3 years ago
isn't b) supposed to be f(x)= -log10(bottom exponent) (3x)? or f(x) = -log10(bottom exponent) (1/3x)? because that is what it is stated from the textbook
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#3
Educator
3 years ago
Quote
b) reflection in the x-axis, horizontal compression by a factor of 1/3.

Yes, sorry. Mistake!

Let's take y = log(bx).

If b is 1 or more, it's a horizontal stretch.
If b is between 0 and 1, we call it a horizontal compression.

In your case, you'd write \(y=-\log \left(\frac{x}{3}\right)\).

What does the textbook state? Its been a while since I've studied this
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#4
Educator
3 years ago
\(y=a\log 10[k(x-d)]+c\)

Where a=the vertical stretch/compression; if a<0, the function has undergone a vertical reflection across the x-axis.

Where c= the vertical shift (upwards or downwards)

Where k=the horizontal stretch/compression; if k<0, the functions has undergone a horizontal reflection across the y-axis.

Where d=the horizontal shift (left or right)


Can you tell me what your textbook reports as the answer?
marinejas Author
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#5
3 years ago
Yes, so for b) the textbook states f(x) = -log10(bottom exponent)(3x)
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#6
Educator
3 years ago
\(y=a\log 10[k(x-d)]+c\)



Your being told in your question "horizontal compression by a factor of 1/3", so we put 1/3 in 1/k to get 1/(1/3) = 3.

That's why we write log(3x)
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