Answer:
–0.83
Step-by-step explanation:
An r-value, or correlation coefficient, tells us the strength of the correlation in a linear regression. This number ranges from -1 to 1; -1 is a perfect linear fit for a decreasing set of data, while 1 is a perfect linear fit for an increasing set of data.
The closer the r-value is to either -1 or 1, the stronger the correlation is.
The two negative numbers we have are -0.83 and -0.67. The first one, -0.83, is 0.17 away from -1. -0.67, on the other hand, is 0.33 away from -1. The two positive numbers we have are 0.48 and 0.79. The first one, 0.48, is 0.52 away from 1. The second one, 0.79, is 0.21 away from 1. The one that is closest to the perfect fit is -0.83, since it is only 0.17 away from a perfect fit.
Answer:
Any expression that doesn't equal 56... You didn't really provide any answer choices, so that's the best answer I have for you...
Answer:
- vertical scaling by a factor of 1/3 (compression)
- reflection over the y-axis
- horizontal scaling by a factor of 3 (expansion)
- translation left 1 unit
- translation up 3 units
Step-by-step explanation:
These are the transformations of interest:
g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k
g(x) = f(x) +k . . . . vertical translation by k units (upward)
g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis
g(x) = f(x-k) . . . . . horizontal translation to the right by k units
__
Here, we have ...
g(x) = 1/3f(-1/3(x+1)) +3
The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:
- vertical scaling by a factor of 1/3 (compression) . . . 1/3f(x)
- reflection over the y-axis . . . 1/3f(-x)
- horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
- translation left 1 unit . . . 1/3f(-1/3(x+1))
- translation up 3 units . . . 1/3f(-1/3(x+1)) +3
_____
<em>Additional comment</em>
The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.
The horizontal transformations could also be described as ...
- translation right 1/3 unit . . . f(x -1/3)
- reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)
The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.
Answer:
24
Step-by-step explanation:
Do i need to explain ??????