Two graphs are drawn, and the function notations for these graphs are f(x) = 2 + 20/x-3 and g(x) = -3 + 32/2x+4
a. Give the formule for the vertical and horizontal asymptotes of the graph of function f
b. Give the formule for the vertical and horizontal asymptotes of the graph of function g
c. Which graph belongs to function f and which belongs to function g?
d. Jasper has drawn the graph for a fractional function. His graph has the line y = -3 as the horizontal asymptote and the line x = 4 as the vertical asymptote. Give a possible function notation for Jasper's graph.
+9466 Assuming that \(f(x)\ =\ 2+\frac{20}{x-3}\) and \(g(x)\ =\ -3+\frac{32}{2x+4}\)
| a.__ | |
| \(y\ =\ f(x)\\~\\ y\ =\ 2+\frac{20}{x-3} \) | |
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| y is undefined when x - 3 = 0 so there is a vertical asymptote at x = 3 |
| \( y-2\ =\ \frac{20}{x-3}\\~\\ (x-3)(y-2)\ =\ 20\\~\\ x-3\ =\ \frac{20}{y-2}\) | |
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| x is undefined when y - 2 = 0 so there is a horizontal asymptote at y = 2 |
| The equations for the vertical and horizontal asymptotes of the graph of f(x) are: x = 3 and y = 2 | |
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b. | |
| \(y\ =\ g(x)\\~\\ y\ =\ -3+\frac{32}{2x+4}\) | |
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| y is undefined when 2x + 4 = 0 so there is a vertical asymptote at x = -2 |
| \(y+3\ =\ \frac{32}{2x+4}\\~\\ (2x+4)(y+3)\ =\ 32\\~\\ 2x+4\ =\ \frac{32}{y+3}\) | |
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| x is undefined when y + 3 = 0 so there is a horizontal asymptote at y = -3 |
| The equations for the vertical and horizontal asymptotes of the graph of g(x) are: x = -2 and y = -3 | |
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c. | |
| Here is a graph: https://www.desmos.com/calculator/7zrrangdvv | |
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| (Note you can hide or show f(x) or g(x) and its asymptotes by clicking the circles beside the function.) |
| Graph 2 belongs to f(x) and graph 1 belongs to g(x) . | |
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d. | |
| A possible function is: \(f(x)\ =\ -3+\frac{1}{x-4}\)_ |
