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Writing rational function from intercepts and asymptotes .

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Final answer:

To write a rational function from intercepts and asymptotes, the y-intercept and slope are used for linear functions, while x-intercepts and vertical asymptotes are incorporated for rational functions with polynomials in the numerator and denominator.

Step-by-step explanation:

Writing a rational function from given intercepts and asymptotes involves using the y-intercept and the slope of a line. The y-intercept is typically represented by the constant term 'a', indicating where the graph crosses the y-axis.

For a linear equation in the slope-intercept form, y = a + bx, 'a' represents the y-intercept and 'b' represents the slope, which is the rate of change, or how much y increases for every increase in x. To create a linear function from these parameters, you would input the known y-intercept for 'a' and slope for 'b'.

If the question pertains to creating a rational function, the process is slightly different. A rational function often takes the form f(x) = \(\frac{P(x)}{Q(x)}\), where P(x) and Q(x) are polynomials. The zeros of P(x) correspond to the x-intercepts of the graph, whereas the zeros of Q(x) correspond to the vertical asymptotes.

To construct a rational function using given intercepts and asymptotes, you would factor in the intercepts to form P(x), and the asymptotes to form Q(x). It's important to note that the y-intercept of a rational function is found by evaluating the function at x = 0.

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