# `y=(2x)/(x^2-1)` Graph the function.

We are asked to graph the function `y=(2x)/(x^2-1) ` :

Factoring the denominator we get:

`y=(2x)/((x+1)(x-1)) `

The graph has vertical asymptotes at x=1 and x=-1. The horizontal asymptote is y=0.

The y-intercept is 0 as is the only x-intercept.

The first derivative is ` y'=(-2(x^2+1))/((x^2-1)^2) ` so the function is decreasing on its domain.

The graph:

Approved by eNotes Editorial Team
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "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, "url": "https://www.enotes.com/homework-help/y-2x-x-2-1-graph-function-818453", "fetch_time": 1670635396000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2022-49/segments/1669446711637.64/warc/CC-MAIN-20221210005738-20221210035738-00436.warc.gz", "warc_record_offset": 774928941, "warc_record_length": 17858, "token_count": 145, "char_count": 436, "score": 3.625, "int_score": 4, "crawl": "CC-MAIN-2022-49", "snapshot_type": "longest", "language": "en", "language_score": 0.8533050417900085, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00063-of-00064.parquet"}