Question

Given the same rational function in standard form from the previous slide. The rational function is both factored (row 1) and simplified (row 2). It is the same rational function as the previous slide. Write the equations for the horizontal asymptote in row 3. Answer the questions in row 4, 5, 6, and 7.

a) Equations for the horizontal asymptote: Bold response required
b) Row 4: Bold response required
c) Row 5: Bold response required
d) Row 6: Bold response required
e) Row 7: Bold response required

Answer 1

A horizontal asymptote for a rational function relates to the degrees and leading coefficients of the numerator and denominator. Without the specific function, a general equation cannot be provided. The line example with slope 3 and y-intercept 9 is described by y = 3x + 9.

Step-by-step explanation:

For a rational function, a horizontal asymptote is determined by the degrees of the polynomials in the numerator and the denominator. When the degrees are equal, the horizontal asymptote is determined by the ratio of the leading coefficients. However, in this case, since the exact rational function isn't provided, a general equation can't be written without additional information.

Regarding the information provided related to the slope-intercept form of a line y = mx + b, where 'm' stands for the slope and 'b' represents the y-intercept, we can deduce that since the line's slope is 3 and the y-intercept is 9, the line equation would be y = 3x + 9.

In algebra, to simplify an equation, such as a rational function, eliminate common factors in the numerator and denominator. Once simplified, always recheck your work to ensure that the results are reasonable and reflect what the function should represent.