Which is the proportional relationship for this graph?
1 answer:
Answer:
For every the canoe is rented, the total cost goes up by $12.
Step-by-step explanation:
To find the proportional relationship, Take two points from the graph, for example (2, 24) and (4, 48), and put them into the slope formula:
Solve:
48 - 24 = 24
4 - 2 = 2
24/2 = 12
The proportional relationship between the hours the canoe is rented and the total cost is $12.
Hope this helps :)
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Answer:
- vertical scaling by a factor of -4
- horizontal translation 5 units left
- vertical translation 11 units up
Step-by-step explanation:
We notice that the multiplier of the squared term in f(x) is 0.5; in g(x), it is -2, so is a factor of -4 times that in f(x).
If we scale f(x) by a factor of -4, we get ...
-4f(x) = -2(x -2)² -12
In order for the squared quantity to be x+3, we have to add 5 to the value that is squared in f(x). That is, x -2 must become x +3. We have to replace x with (x+5) to do that, so ...
(x+5) -2 = x +3
The replacement of x with x+5 amounts to a translation of 5 units to the left.
We note that the added constant after our scaling changes from +3 to -12. Instead, we want it to be -1, so we must add 11 to the scaled function. That translates it upward by 11 units.
The attached graph shows the scaled and translated function g(x):
g(x) = -4f(x +5) +11
