mathdad
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- Apr 24, 2015
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In the problem below, follow Steps 1 through 8 on to analyze the graph of the function.
STEP 1:
Factor the numerator and denominator of R. Find the domain of the rational function.
STEP 2:
Write R in lowest terms.
STEP 3:
Locate the intercepts of the graph. The x-intercepts are the zeros of the numerator of R that are in the domain of R. Determine the behavior of the graph of R near each x-intercept.
STEP 4:
Determine the vertical asymptotes. Graph each vertical asymptote using a dashed line.
STEP 5:
Determine the horizontal or oblique asymptote, if one exists. Determine points, if any, at which the graph of R intersects this asymptote. Graph the asymptote using a dashed line. Plot any points at which the graph of R intersects the asymptote.
STEP 6:
Use the 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. Plot the points found.
STEP 7:
Analyze the behavior of the graph of R near each asymptote and indicate this behavior on the graph.
STEP 8:
Use the results obtained in Steps 1 through 7 to graph R.
R(x) = (3x + 3)/(2x + 4)
Can you explain, in easy terms, steps 5 through 7?
STEP 1:
Factor the numerator and denominator of R. Find the domain of the rational function.
STEP 2:
Write R in lowest terms.
STEP 3:
Locate the intercepts of the graph. The x-intercepts are the zeros of the numerator of R that are in the domain of R. Determine the behavior of the graph of R near each x-intercept.
STEP 4:
Determine the vertical asymptotes. Graph each vertical asymptote using a dashed line.
STEP 5:
Determine the horizontal or oblique asymptote, if one exists. Determine points, if any, at which the graph of R intersects this asymptote. Graph the asymptote using a dashed line. Plot any points at which the graph of R intersects the asymptote.
STEP 6:
Use the 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. Plot the points found.
STEP 7:
Analyze the behavior of the graph of R near each asymptote and indicate this behavior on the graph.
STEP 8:
Use the results obtained in Steps 1 through 7 to graph R.
R(x) = (3x + 3)/(2x + 4)
Can you explain, in easy terms, steps 5 through 7?
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