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tonydeanfbg8706
20.12.2020 •
Mathematics
Write a rational function with an x-intercept at (-9,0), a vertical asymptote at x=3, and a hole located at (1,-5). Then, identify the horizontal asymptote.
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Ответ:
The rational function is![f(x) = \dfrac{x^2 + 8\cdot x - 9}{x^2 - 4 \cdot x + 3}](/tpl/images/1003/1050/1ff63.png)
The horizontal asymptote occur at y = 1
Step-by-step explanation:
Given that the function has an x-intercept at (-9, 0), we have;
(x + 9) is a factor of the function
Also, given that the function has a vertical asymptote at x = 3, we have that a factor of the denominator of the function is (x - 3)
With a hole at (1, -5), we have, (x - 1) in both the numerator and the denominator and when x = 1, f(x) = -5
The general form of the function can be presented as follows;
f(x) = ((x + 9)·(x - 1))/((x - 3)(x - 1)) = (x² + 8·x - 9)/(x² - 4·x + 3)
Given that the power of the numerator and the denominator are equal, the horizontal asymptote occur at ratio of the leading coefficient of the numerator and the denominator which from the above equation is 1/1 = 1
The horizontal asymptote occur at y = 1
Please find attached the graph of the function created with Microsoft Excel
Ответ:
Step-by-step explanation:
The triangular prism shown has 2 triangular face(s) and 3 lateral face(s).
The area of one triangular face is 7.5 mm2.
The surface area of the triangular prism is 135 mm2.