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Chapter 8: Q. 11 (page 556)

Analyze the graph of the rational function

Rx=2x2-7x-4x2+2x-15

Short Answer

Expert verified

The domain of the function is x|x鈮�-5,x鈮�3.

Its intercepts are -12,0,4,0,0,415.

The asymptotes of the function are aty=-5,y=3,x=2

Step by step solution

01

Step 1. Given Information

The given expression isRx=2x2-7x-4x2+2x-15.

02

Step 2. Find the Domain

  • Find the factors of the expression in the numerator and the denominator.

Rx=2x+1x-4x+5x-3

  • The denominator will become 0 if the value of xis -5or 3.
  • So, the domain of the function isx|x鈮�-5,x鈮�3.
03

Step 3. Find The Intercepts

  • The numerator of the function becomes 0 when the value of xis -12,4.
  • So, the x-intercepts are -12,0,4,0.
  • The value of R(0)=415/
  • So, the y-intercept is 0,415.
04

Step 4. Find the Asymptotes

  • The denominator becomes 0 at-5,3.
  • So, the vertical asymptotes are x=-5,x=3.
  • The ratio of leading coefficients of the numerator and denominator is 2.
  • So, the vertical asymptote isy=2.
05

Step 5. Plot the Graph

Use the information above to plot the following graph.

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