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.There is a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. The first curve passes through the points left-parenthesis negative 3 comma Start Fraction negative 1 over 3 End Fraction right-parenthesis, left-parenthesis negative 2 comma negative one half right-parenthesis, left-parenthesis negative 1 comma negative 1 right-parenthesis, and left-parenthesis negative one half comma negative 2 right-parenthesis. The second curve passes through points left-parenthesis one half comma 2 right-parenthesis, left-parenthesis 1 comma 1 right-parenthesis, left-parenthesis 2 comma one half right-parenthesis, and 3 comma Start Fraction 1 over 3 End Fraction right-parenthesis.
Image with alt text: A function is graphed on the coordinate plane that consists of two curves. There is a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. The first curve passes through the points left-parenthesis negative 3 comma Start Fraction negative 1 over 3 End Fraction right-parenthesis, left-parenthesis negative 2 comma negative one half right-parenthesis, left-parenthesis negative 1 comma negative 1 right-parenthesis, and left-parenthesis negative one half comma negative 2 right-parenthesis. The second curve passes through points left-parenthesis one half comma 2 right-parenthesis, left-parenthesis 1 comma 1 right-parenthesis, left-parenthesis 2 comma one half right-parenthesis, and 3 comma Start Fraction 1 over 3 End Fraction right-parenthesis.

Answer 1

The graph of the parent reciprocal function \( f(x) = \frac{1}{x} \) consists of two curves with a vertical asymptote at \( x = 0 \) and a horizontal asymptote at \( y = 0 \).

Based on the descriptions provided, the correct answer is:

A function is graphed on the coordinate plane that consists of two curves. There is a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. The first curve passes through the points \( (-3, -\frac{1}{3}) \), \( (-2, -\frac{1}{2}) \), \( (-1, -1) \), and \( (-\frac{1}{2}, -2) \). The second curve passes through points \( (\frac{1}{2}, 2) \), \( (1, 1) \), \( (2, \frac{1}{2}) \), and \( (3, \frac{1}{3}) \).

This reflects the characteristics of the reciprocal function.