Which graph represents the function f (x) = StartFraction 3 x minus 2 Over x minus 2 EndFraction?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = negative 2, and the horizontal asymptote is at y = 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

Question

6612020096 6612020096

11-07-2022
Mathematics

contestada

Which graph represents the function f (x) = StartFraction 3 x minus 2 Over x minus 2 EndFraction?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = negative 2, and the horizontal asymptote is at y = 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

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adioabiola adioabiola · Answer 1 · 2022-07-12T20:44:45+02:00

The graph which represents the rational function is; On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

Which graph represents the rational function?

It follows from the task content that the rational function given is; f(x) = 3x-2/x-2.

Hence, since the numerator and denominator polynomials are of the same order, it follows that the horizontal asymptote is the quotient; 3/1 = 3.

Additionally, the vertical asymptote of the function is the value of x which renders the denominator equal to 0 and consequently, the function undefined.

Hence, x -2 = 0 and x= 2.