- 7 Follow The Steps For Graphing A Rational Function To Graph The Function R X X 16 If Needed First Write The G 1 (8.52 KiB) Viewed 37 times
If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of R(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type your answer in factored form. Do not simplify.) A. R(x) = B. R(x) is already in factored form.
What is the domain of R(x)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. {x|x ² B. {x|X< (Type an integer or a simplified fraction.) (Type an integer or a simplified fraction.) OC. {X/x*} (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers.
Write R(x) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. R(x) = (Simplify your answer.) B. R(x) is already in lowest terms.
Locate the intercept(s) of the graph. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The graph has x-intercept(s) and y-intercept (Simplify your answers. Type integers or fractions. Use a comma to separate answers as needed. Type each answer only once.) B. The graph has y-intercept and no x-intercept. (Simplify your answer. Type an integer or a fraction.) C. The graph has x-intercept(s) and no y-intercept. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) D. The graph has neither x-intercepts nor y-intercepts.
Determine the behavior of the graph of R at any x-intercepts. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The graph will cross the x-axis at x = and touch but not cross the x-axis at x = (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. The graph will touch but not cross the x-axis at x = (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) C. The graph will cross the x-axis at x = (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) OD. There is no x-intercept.
Determine the vertical asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is , and the rightmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) OC. The function has three vertical asymptotes. The leftmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) D. There is no vertical asymptote. the middle asymptote is and the rightmost asymptote is
Determine the vertical asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is , and the rightmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) OC. The function has three vertical asymptotes. The leftmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) D. There is no vertical asymptote. the middle asymptote is and the rightmost asymptote is
Determine the behavior of the graph on either side of any vertical asymptotes, if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. It approaches ∞ on one side of the asymptote(s) at x = and - ∞ on the other. It approaches either ∞ or -∞ on both sides of the asymptote(s) at x = (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. It approaches ∞ on one side of the asymptote(s) at x = and on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. It approaches either ∞ or -∞ on both sides of the asymptote(s) at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) OD. There is no vertical asymptote.
Determine the horizontal asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no horizontal asymptote.
Determine the oblique asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one oblique asymptote, (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two oblique asymptotes. The oblique asymptote with a negative slope is (Type equations. Use integers or fractions for any numbers in the equations.) OC. There is no oblique asymptote. and the oblique asymptote with a positive slope is
Determine the points, if any, at which the graph of R intersects the horizontal or oblique asymptote, if one exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The graph of R intersects the horizontal or oblique asymptote at (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) B. The graph of R intersects the horizontal or oblique asymptote at infinitely many points. C. There is no point at which the graph of R intersects the horizontal or oblique asymptote. D. There is no horizontal or oblique asymptote.
Use the real zeros of the numerator and denominator of R to divide the x-axis into intervals. Determine where the graph of R is above or below the x-axis by choosing a number in each interval and evaluating R there. Select the correct choice below and fill in the answer box(es) to complete your choice. OA. The graph of R is above the x-axis on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) B. The graph of R is below the x-axis on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) C. The graph of R is above the x-axis on the interval(s) and below the x-axis on the interval(s) (Type your answers in interval notation. Use a comma to separate answers as needed.)
Use the results from the previous steps to graph R. Choose the correct graph below. A. O B. 4. O C. X D. Ⓒ