f (x) = 3x + 5
[1] Solve the following equation: (refer to the photo below). Kindly follow the steps in graphing a rational function.
Step 1: Find the vertical asymptotes. This is done by equating the denominator to 0 and then solve for x. The value of x will be the asymptote.
Step 2: Find the horizontal asymptotes. a) If the degree or the highest exponent of the variable of the denominator is higher than the degree of the numerator, then the horizontal asymptote is y = 0 or the x-axis. b) If the degree of the numerator is higher than the degree of the denominator, then there is no horizontal asymptote but rather, a salnt or oblique asymptote. To find the slant or oblique asyptote, divide the numerator by the denominator using either the long division or the synthetic division. The slant or oblique asymptote is the polynomial part of the quotient. c) If the degree of the numerator is equal to the degree of the denoinator, the horizontal asymptote is equal to the leading coefficient of the numerator divided by the leading coefficient of the denominator.
Step 3: Find the x - and y - intercept, if any. To find x - intercept(s), set y = 0. To find the y - intercept(s), set x = 0.
Step 4: Plot as many points as necessary in each interval.
Step 5: Sketch the graph.
Step by step
Solved in 5 steps with 2 images
