Determine the vertical asymptote for the rational function f(x) = x-4 over 3x +2

Mathematics

1 answer:

Ghella [55]3 years ago

8 0

Answer: (b) x = -2/3

<u>Step-by-step explanation:</u>

The vertical asymptote is the restriction on x.

The denominator cannot be equal to zero so that it the restriction.

Set the denominator equal to zero and solve for x to find the asymptote.

3x + 2 = 0

3x = -2

x = -2/3

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a) Y(x) = {900, x≤30; 900-40(x-30), x>30}

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_____

The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.