Precalculus
Topics

# How do you find the horizontal asymptote for y = x / (x-3)?

Jul 11, 2018

$\text{horizontal asymptote at } y = 1$

#### Explanation:

$\text{Horizontal asymptotes occur as}$

${\lim}_{x \to \pm \infty} , y \to c \text{ (a constant)}$

$\text{divide terms on numerator/denominator by } x$

$y = \frac{\frac{x}{x}}{\frac{x}{x} - \frac{3}{x}} = \frac{1}{1 - \frac{3}{x}}$

$\text{As } x \to \pm \infty , y \to \frac{1}{1 - 0}$

$y = 1 \text{ is the asymptote}$
graph{x/(x-3) [-10, 10, -5, 5]}

##### Impact of this question
981 views around the world
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7591816186904907, "perplexity": 6129.689718028063}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038078021.18/warc/CC-MAIN-20210414185709-20210414215709-00321.warc.gz"}