A rational function is given by the function equation: R(x) = 2x+4x 16x x3 - x...

 

Transcribed Image Text:

A rational function is given by the function equation: R(x) = 2x³+4x² 16x x3 - x² - 2x All the solutions and explanations should be given without using a graphing calculator! (a) Factor the denominator and determine the domain of the function. (b) Factor the numerator and simplify the function to the lowest terms. (c) Find all the x- and y- intercepts, if any. (d) Find the vertical asymptotes, if any. (e) Find the horizontal or oblique asymptotes, if any. (f) For each x-intercept, determine whether the graph of the function is crossing or touching. Explain how you know by using multiplicities. (g) For each vertical asymptote determine how the graph of the function is approaching the asymptote. Explain how you know by using multiplicities. (h) Sketch the graph of the function by hand. Label each hole, if any. A rational function is given by the function equation: R(x) = 2x³+4x² 16x x3 - x² - 2x All the solutions and explanations should be given without using a graphing calculator! (a) Factor the denominator and determine the domain of the function. (b) Factor the numerator and simplify the function to the lowest terms. (c) Find all the x- and y- intercepts, if any. (d) Find the vertical asymptotes, if any. (e) Find the horizontal or oblique asymptotes, if any. (f) For each x-intercept, determine whether the graph of the function is crossing or touching. Explain how you know by using multiplicities. (g) For each vertical asymptote determine how the graph of the function is approaching the asymptote. Explain how you know by using multiplicities. (h) Sketch the graph of the function by hand. Label each hole, if any.