Which is the graph of the parent reciprocal function?

Question

(1 point)
Responses

A diagonal line is graphed on the coordinate plane. It passes through points left parenthesis negative 2 comma negative 2 right parenthesis, left-parenthesis negative 1 comma negative 1 right-parenthesis, left parenthesis 0 comma 0 right parenthesis, left-parenthesis 1 comma 1 right-parenthesis, and left parenthesis 2 comma 2 right parenthesis.
Image with alt text: A diagonal line is graphed on the coordinate plane. It passes through points left parenthesis negative 2 comma negative 2 right parenthesis, left-parenthesis negative 1 comma negative 1 right-parenthesis, left parenthesis 0 comma 0 right parenthesis, left-parenthesis 1 comma 1 right-parenthesis, and left parenthesis 2 comma 2 right parenthesis.

A horizontal line is graphed on the coordinate plane. Points are shown on the line at x-values of negative 2, negative 1, 0, 1 and 2. The point left parenthesis 0 comma c right parenthesis is labeled.
Image with alt text: A horizontal line is graphed on the coordinate plane. Points are shown on the line at x-values of negative 2, negative 1, 0, 1 and 2. The point left parenthesis 0 comma c right parenthesis is labeled.

A v-shaped graph is shown on the coordinate plane. It passes through the points left-parenthesis negative 2 comma 2 right-parenthesis, left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis 1 comma 1 right-parenthesis, and left-parenthesis 2 comma 2 right-parenthesis.
Image with alt text: A v-shaped graph is shown on the coordinate plane. It passes through the points left-parenthesis negative 2 comma 2 right-parenthesis, left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis 1 comma 1 right-parenthesis, and left-parenthesis 2 comma 2 right-parenthesis.

A function is graphed on the coordinate plane that consists of two curves.

Answer 1

The parent reciprocal function is represented by the equation \( f(x) = \frac{1}{x} \). The graph of this function features two branches that approach the x-axis and y-axis but never touch them, creating vertical and horizontal asymptotes. It is characterized by values that decrease as x moves towards zero from the right (approaching \( +\infty \)) and increase as x approaches zero from the left (approaching \( -\infty \)).

Based on the descriptions you provided, none of the graphs match the characteristics of the parent reciprocal function. The descriptions you gave include a diagonal line, a horizontal line, a v-shaped graph, and a function with two curves—none of which represent the reciprocal function's typical hyperbolic shape.

If you need clarification or further information regarding the parent reciprocal function and its graph, feel free to ask!