Question

Find the equation
PLEASE HELP QUICK

Answer 1

`y=(1)/(x-4)-2`

Explanation:

The given graph represents a rational function with specific characteristics:

• Vertical asymptote: x = 4
• Horizontal asymptote: y = -2
• x-intercept = (4.5, 0)

The shape of the curve resembles a reciprocal function in the form of

`y=(a)/(x-h)+k`

where:

• x = h is the vertical asymptote.
• y = k is the horizontal asymptote.
• a is a constant.

As the vertical asymptote is x = 4, then h = 4.

As the horizontal asymptote is y = -2, then k = -2.

Substituting these values into the equation, we get:

`y=(a)/(x-4)-2`

To find the value of a, we can substitute the point on the curve (4.5, 0) into the equation and solve for a:

`0=(a)/(4.5-4)-2`

`2=(a)/(0.5)`

`1=a`

Finally, substituting the value of a = 1 back into the equation, we can write the equation of the graphed curve as:

`\large\boxed{\boxed{y=(1)/(x-4)-2}}`