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Suppose c and y vary together such that y= 4x + 8. a. Suppose x varies from x= 2 to x= 7.5. i. Over this interval, how much does x change by? ii. Over this interval, how much does y change by? iii. Over this interval, the change in y is how many times as large as the change in x? b. Suppose x varies from x= -5.1 to x= -5.1. i. Over this interval, how much does x change by? ii. Over this interval, how much does y change by? iii. Over this interval, the change in y is how many times as large as the change in x?

Respuesta :

sqdancefan

Answer:

  ai) 5.5

  aii) 22

  aiii) 4

  bi) 0

  bii) 0

  biii) undefined

Step-by-step explanation:

ai) The change in x is x2 -x1 = 7.5 -2 = 5.5 . . . . change in x

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aii) The change in y is (4(7.5) +8) -(4(2) +8) = 4(7.5-2) = 22.0 . . . . change in y

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aiii) The ratio of changes is (change in y)/(change in x) = 22/5.5 = 4

The change in y is 4 times the change in x.

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bi) The difference is -5.1 -(-5.1) = 0 . . . . change in x

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bii) The difference is (4(-5.1)+8) -(4(-5.1)+8) = 0 . . . . change in y

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biii) The ratio of changes is (change in y)/(change in x) = 0/0 = undefined.

The multiplier of the change in x to get the change in y is undefined.

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Comment on part B

We know that the relative rates of change for x and y in this linear function are 1 : 4. However, we cannot compute that ratio directly when the change in x is 0. (The ratio holds for vanishingly small values of change in x, so is 4 in the limit as Δx → 0. That isn't what the problem asks.)

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