What is the value of m in the equation 1/2m-3/4n=16, when n = 8?
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We are given: Price of stock on 1st January = $10.
And price of stock on 31st january = $12.
Let us represent Day number and Price by coordinate (x,y).
Therefore, coordinates for January month can be written as (1,10) and (31,12).
Price of stock on 1st February = $10.
And price of stock on 28th February = $9.
Let us represent Day number and Price by coordinate (x,y).
Therefore, coordinates for February month can be written as (1,12) and (28,9).
Now, we can plot those two different pairs of coordinates for January and February on the graph.
From the graph, we can see that slope of red line is greater and it is positive and slope of green line is negative(because price decreasing).
Therefore, the price change from $10 to $9 is not a straight line.
Therefore, we can say from January 1 to January 31 the rate is inceasing so the slope is positive then after 1 February the rate started decreasing so the slope became negative.
The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
- vertical stretch of 0.35
- horizontal compression of period of
- phase shift of
to right
The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is A, assuming horizontal axis is input axis and vertical is for outputs, then:
- Horizontal shift (also called phase shift):
- Left shift by c units: earlier)
- Right shift by c units:
output, but c units late)
- Vertical shift:
- Up by d units:
- Down by d units:
- Stretching:
- Vertical stretch by a factor k:
- Horizontal stretch by a factor k:
For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to
We can see its vertical stretch by 0.35, right shift by horizontal stretch by 1/8
Period of cos(x) is of length. But 1.8 stretching makes its period shrink to
Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35
horizontal compression to period of (which means period of cosine is shrunk to which originally was )
phase shift of to right
Learn more about transformation of functions here: