Sketch the graph of each rational function showing all the key features. Verify your graph by graphing the function onthe graphing calculator.1. f(x) = 4x − 6 / 2x + 5

Answer:The Answer is:Domain of the function: Dom= {x ∈ R: x ≠ [tex]\frac{-5}{2}[/tex]}Horizontal asymptote: y=2Vertical asymptote: x=[tex]\frac{-5}{2}[/tex]Cut with X-axis: x=[tex]\frac{-6}{5}[/tex]Step-by-step explanation:1. Domain of the function: To find the domain of the function you have to find where the dominator of the function is ZERO, so you have to make 2x+5=02x+5=02x=-5x=-5/2 Thats the point of the graph that does NOT existThe domain of the function is: all real numbers except (-5/2) Dom= {x ∈ R: x ≠ [tex]\frac{-5}{2}[/tex]}2. Horizontal asymptote: take the first numbers that are with the X's in this case: 4x− 6/ 2x+5 you have to take 4x and 2x so y=4/23. Vertical asymptote: take the number of 1. and thats the vertical asymptote in this case is x=-5/24. Cut with X-axis: replace the x by zero, f(0) = 4(0) − 6 / 2(0) + 5f(0)=-6/5, f(x)=-6/5this are the key features of the graph now you can replace numbers and draw your graph