Graphs of Rational Functions
Graphs of rational functions are essential in understanding the behavior of functions that can be expressed as the ratio of two polynomials. These graphs often exhibit unique features, such as asymptotes and intercepts, which provide insights into the function's behavior. By analyzing these graphs, one can determine key characteristics, such as domain, range, and end behavior, which are crucial for understanding the overall function. Additionally, studying the graphs of rational functions helps in solving real-world problems, as these functions can model various phenomena, such as population growth, economics, and physics, making them valuable tools in mathematical analysis and modeling.
Questions
- How do you graph #(2x)/(x-4)#?
- How do you graph #f(x)=4/(x-1)+1# using holes, vertical and horizontal asymptotes, x and y intercepts?
- How do you graph #f(x)=(x^2-5x+6)/(x^2-4x+3)# using holes, vertical and horizontal asymptotes, x and y intercepts?
- How do you graph #f(x)=-2/(x^2+x-2)# using holes, vertical and horizontal asymptotes, x and y intercepts?
- How do you write an equation for a rational function that has a vertical asymptote at x=2 and x=3, a horizontal asymptote at y=0, and a y-intercept at (0,1)?
- How do you graph #f(x)= (x^2-100)/(x+10)#?
- How do you graph #(x^2-4)/(x^2-9)#?
- How do you find the zeros of the function #f(x)=(20x^2+11x-40)/(2x+5)#?
- How do you graph #f(x)=-3/(x-1)-1# using holes, vertical and horizontal asymptotes, x and y intercepts?
- What are the asymptotes of #y=1/(x-2)# and how do you graph the function?
- How do you graph #(x^2+3x-4)/x#?
- How do you find the zeros of the function #f(x)=(x^2+3x-4)/(x^2+9x+20)#?
- How do you graph #f(x)=(x-2) / (x+2)#?
- Which quadrant does # y=x/(x^2+2x+1)# lie?
- How do you graph #R(x) = (x + 2)/(x^2 - 4)#?
- How do you graph #f(x)=2/(x^2-4x+4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
- How do you graph and find the discontinuities of #(x^2-1)/(x^2+4)#?
- How do you graph and find the discontinuities of #1 /(x+6)#?
- How do you graph #y= (2x)/(x-1)#?
- How do you graph #f(x)=3/(x^2(x+5))# using holes, vertical and horizontal asymptotes, x and y intercepts?