The function f(x) is defined as, [tex]f(x) = 3 + \frac{1}{2x-5}[/tex], x ≠ [tex]\frac{5}{2}[/tex](a) Sketch the curve of f for -5 ≤ x ≤ 5, showing the asymptotes.(b) Using your sketch, write down (i) the equation of each asymptote; (ii) the value of the x-intercept; (iii) the value of the y-intercept.Image attached.

Answer:a) look at the figureb) i) x = 2.5 , y = 3    ii) x-intercept is 2.333    iii) y-intercept is 2.8Step-by-step explanation:a) The points of the graph f(x) = 3+1/2x - 5 are:f(-5) = 2.9333f(-4) = 2.923f(-3) = 2.909f(-2) = 2.888f(-1) = 2.857f(0) = 2.8f(1) = 2.666f(2) = 2f(3) = 4f(4) = 3.333f(5) = 3.2b)i) to find the vertical asymptotic put the denominator = 0   2x - 5 = 0 ⇒ 2x = 5 ⇒ x = 5 ÷ 2 = 2.5∴ The equation of the vertical asymptotic is x = 2.5To find the horizontal asymptotic look at the degree of the numerator and denominator∵ they are equal f(x) = (6x -14)/(2x - 5) ⇒ 6x ÷ 2x = 3∴ The equation of the horizontal asymptotic is y = 3ii) the value of x-intercept means put f(x) = 0∴3 + 1/2x - 5 = 0 ⇒ 1/2x - 5 = -3 ⇒ -6x + 15 = 1 ⇒ 6x = 14   x = 14/6 = 2.333iii) The value of y-intercept means x = 0∴ f(x) = 3 + 1/0 - 5 = 3 + (-0.2) = 2.8