Question

Which graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1? 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 = 0, and the horizontal asymptote is at y = 1. 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 = 1, and the horizontal asymptote is at y = 0. 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 = negative 1, and the horizontal asymptote is at y = 0. 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 = 0, and the horizontal asymptote is at y = negative 1.

Answer 1

Answer:

Step-by-step explanation:Answer:

D

Step-by-step explanation:

right on edge

Answer 2

Option D :

• The given Hyperbola curve opens in Quadrants 1 and 3
• The vertical asymptote is at "x = 0"
• The Horizontal asymptote is at "y = -1"

Horizontal and Vertical Asymptotes of any Graph :

• A vertical asymptote of a graph is any vertical line of the form "x = a" such that the graph tends toward positive or negative infinity as the input "x" approaches "a".
• A horizontal asymptote of a graph on the other hand is any horizontal line of the form "y = b" such that the graph tends towards the line when the input "x" tends to the value "a".

The function of the graph as given in the question is :

               $f(x) = (1/x)-1$

Finding Vertical Asymptote :

For vertical asymptote, we need to find any value "a" of x putting which the function tends to either side of infinity.

      i.e.      $f(a) = (1/a) - 1$   such that $f(a)$⇒∞, -∞

                ∞, -∞  $= (1/a)-1$

                ∞, -∞  $= (1/a)$

                $a$ ⇒ 0

Thus, when "x" tends to 0, the function tends to infinity. So, the Vertical Asymptote of the given graph is "x=a" i.e. "x=0".

Finding Horizontal Asymptote :

For Horizontal asymptote, we need to find any value "b" of y which is the function value on putting "x" with value "a".

      i.e.      $b = f(a)$  

                 $b = (1/a)-1$

                 $b = (1/0)-1$

                 $b = -1$

             

Thus, when "x" tends to a, the function approaches the graph "y=b". So, the Horizontal Asymptote of the given graph is "y=b" i.e. "y=-1".

Hence, Option D is correct stating "x=0" as the vertical asymptote and "y=-1" as the horizontal asymptote.

To learn more about Asymptotes, visit

https://brainly.in/question/55681400

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