How many triangles exist with the given side lengths? 4m, 4m, 7m.
2 answers:
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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:
Point slope form is used when we have the information of at least two coordinates that lie on the line
For example:
Given that coordinate (3, 4) and (6, 7) lies on a straight line.
We work out the equation of the line by substituting the two coordinates into the formula (y - y₁) = m(x - x₁) where (x₁, y₁) could be either (3, 4) and (6, 7).
We would need to use both coordinates to work out the gradient (m) by using the formula:
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The slope intercept form is used when we are given enough information to work out the gradient as well as the y-intercept.
For example:
Given two coordinates (3, 5) and (0, 9)
This information can help to find the gradient and the y-intercept.
The y-intercept would be at 9 because the (0, 9)
We calculate the gradient m
Then substitute into y=mx+c which is the slope intercept form.
For example:
Given that coordinate (3, 4) and (6, 7) lies on a straight line.
We work out the equation of the line by substituting the two coordinates into the formula (y - y₁) = m(x - x₁) where (x₁, y₁) could be either (3, 4) and (6, 7).
We would need to use both coordinates to work out the gradient (m) by using the formula:
----------------------------------------------------------------------------------------------------------------
The slope intercept form is used when we are given enough information to work out the gradient as well as the y-intercept.
For example:
Given two coordinates (3, 5) and (0, 9)
This information can help to find the gradient and the y-intercept.
The y-intercept would be at 9 because the (0, 9)
We calculate the gradient m
Then substitute into y=mx+c which is the slope intercept form.