Question

Determine each feature of the graph of the given function.

Horizontal Asymptote:

Vertical Asymptote:

x-Intercept:

y-Intercept:

Hole:

Answer 1

Horizontal Asymptote: x = 0

Vertical Asymptote:

2x² + 13x + 20 = 0

(x + 4)(2x + 5) = 0

x = -2.5 (x = -4 is a hole)

x-intercept:

4x + 16 = 0

4x = -16

x = -4

Since x = -4 is a hole, this graph has no x-intercepts.

y-intercept: f(0) = 16/20 = 4/5

hole: x = -4

`\frac{4x + 16}{2 {x}^(2) + 13x + 20 } = (4(x + 4))/((x + 4)(2x + 5)) = (4)/(2x + 5)`