Question

17. Write a rational function in expanded form that satisfies the

following criteria:
• V.A. x=2
• SI.A y =5x-1
• Zero of function (-1,0)

pls help thank you<3

Answer 1

`f(x) = (5x^2 + 4x - 1)/(x - 2)`

Explanation:

Given

VA;
`x = 2`

SLA:
`y = 5x - 1`

Zero of function:
`(-1,0)`

Required

Determine the rational function in expanded form

Analyzing the vertical asymptote

The vertical asymptote is given as:

`x = 2`

Subtract 2 from both sides

`x - 2 = 2 - 2`

`x - 2 = 0`

This means that the denominator must be
`x - 2`

Analyzing the zero of the function

The zero of the function is given as:
`(-1,0)`

This means that
`x = -1`, when
`y = 0`

Equate
`x = -1` to 0 by add 1 to both sides

`x + 1 =- 1 + 1`

`x + 1 =0`

This means that one of the numerators must be
`x + 1`

Analyzing the slant asymptote:

`y = 5x - 1`

This means that one of the numerators must be
`5x - 1`

Hence, the function is:

`f(x) = ((5x - 1)(x+1))/(x - 2)`

Expand the numerator

`f(x) = (5x^2 + 5x - x - 1)/(x - 2)`

`f(x) = (5x^2 + 4x - 1)/(x - 2)`