Answer:
a) look at the figure
b) i) x = 2.5 , y = 3
ii) x-intercept is 2.333
iii) y-intercept is 2.8
Step-by-step explanation:
a) The points of the graph f(x) = 3+1/2x - 5 are:
f(-5) = 2.9333
f(-4) = 2.923
f(-3) = 2.909
f(-2) = 2.888
f(-1) = 2.857
f(0) = 2.8
f(1) = 2.666
f(2) = 2
f(3) = 4
f(4) = 3.333
f(5) = 3.2
b)
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 = 2.5
To 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 = 3
ii) 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 = 2.333
iii) The value of y-intercept means x = 0
∴ f(x) = 3 + 1/0 - 5 = 3 + (-0.2) = 2.8
![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 asymptot class=](https://us-static.z-dn.net/files/de4/9bbe7ea72d46c40ffbea88bb8b630757.jpg)
