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
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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
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<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:
Eric, 9.8 meters.
Step-by-step explanation:
Use the distance formula with the given coordinate and each of the other coordinate.
Brooke
Eric
Cam
You'll see that Eric kicked the furthest distance with a distance of 9.8 meters.
Brooke kicked 9.2 meters and Cam kicked 9.4 meters. What does the distance formula really mean? When you solve for the distance between two points, you're really just creating a triangle between those two points, and you're actually looking for the hypotenuse. The slope that intersects your two points is the hypotenuse of the triangle you created.
Answer: It should be the third one
Step-by-step explanation:
Answer:
the first one I guess
Step-by-step explanation:
Answer:
<h2>-8(k - 4) = -8k + 32</h2>
Step-by-step explanation:
-8(k - 4) <em>use the distributive property: a(b + c) = ab + ac</em>
= (-8)(k) + (-8)(-4) = -8k + 32