Answer:
The Answer is:
Domain of the function: Dom= {x ∈ R: x ≠ [tex]\frac{-5}{2}[/tex]}
Horizontal asymptote: y=2
Vertical 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=0
2x+5=0
2x=-5
x=-5/2 Thats the point of the graph that does NOT exist
The 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=4/2
3. Vertical asymptote: take the number of 1. and thats the vertical asymptote in this case is x=-5/2
4. Cut with X-axis: replace the x by zero, f(0) = 4(0) − 6 / 2(0) + 5
f(0)=-6/5, f(x)=-6/5
this are the key features of the graph now you can replace numbers and draw your graph
