**Consider the following function.**$ q(x) = \frac{x - 2}{5x - 1} $Find the horizontal intercept and the vertical intercept of the function. (If an answer does not exist, enter DNE.)- Horizontal intercept $(x, y) = (\ \ \ \ \ \ ,\ \ \ \ \ \ )$- Vertical intercept $(x, y) = (\ \ \ \ \ \ ,\ \ \ \ \ \ )$Find the vertical asymptotes and the horizontal or slant asymptotes of the function. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.)- Vertical asymptote(s) $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ - Horizontal or slant asymptote(s) $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$**Sketch the graph.**Below are four graph options for the function:1. **Graph A**: Shows a vertical asymptote at $x = \frac{1}{5}$ with the curve approaching infinity as it nears this line. The horizontal asymptote appears to be $y = \frac{1}{5}$.2. **Graph B**: Similar vertical and horizontal asymptotes as Graph A, but with the curve differently approaching the asymptotes.3. **Graph C**: Also has a vertical asymptote at $x = \frac{1}{5}$, but the graph features different curve behavior compared to the others.4. **Graph D**: Matches the vertical asymptote at $x = \frac{1}{5}$, with a curve behavior distinct from other options.Select the graph that accurately represents the function $ q(x) = \frac{x - 2}{5x - 1} $.

Consider the following function. x - 2 q(x) = 5x - 1 Find the horizontal intercept and the vertical intercept of the function. (If an answer does not exist, enter DNE.) horizontal intercept (x, y) = vertical intercept (x, y) = Find the vertical asymptotes and the horizontal or slant asymptotes of the function. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.) vertical asymptote(s) horizontal or slant asymptote(s) Sketch the graph.

Consider the following function. x - 2 q(x) = 5x - 1 Find the horizontal intercept and the vertical intercept of the function. (If an answer does not exist, enter DNE.) horizontal intercept (x, y) = vertical intercept (x, y) = Find the vertical asymptotes and the horizontal or slant asymptotes of the function. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.) vertical asymptote(s) horizontal or slant asymptote(s) Sketch the graph.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Consider the following function.**

$ q(x) = \frac{x - 2}{5x - 1} $

Find the horizontal intercept and the vertical intercept of the function. (If an answer does not exist, enter DNE.)

- Horizontal intercept $(x, y) = (\ \ \ \ \ \ ,\ \ \ \ \ \ )$
- Vertical intercept $(x, y) = (\ \ \ \ \ \ ,\ \ \ \ \ \ )$

Find the vertical asymptotes and the horizontal or slant asymptotes of the function. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.)

- Vertical asymptote(s) $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$
- Horizontal or slant asymptote(s) $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

**Sketch the graph.**

Below are four graph options for the function:

1. **Graph A**: Shows a vertical asymptote at $x = \frac{1}{5}$ with the curve approaching infinity as it nears this line. The horizontal asymptote appears to be $y = \frac{1}{5}$.

2. **Graph B**: Similar vertical and horizontal asymptotes as Graph A, but with the curve differently approaching the asymptotes.

3. **Graph C**: Also has a vertical asymptote at $x = \frac{1}{5}$, but the graph features different curve behavior compared to the others.

4. **Graph D**: Matches the vertical asymptote at $x = \frac{1}{5}$, with a curve behavior distinct from other options.

Select the graph that accurately represents the function $ q(x) = \frac{x - 2}{5x - 1} $.

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