What is the horizontal asymptote of y = x+1/x-1?

Worked solution for TMUA-P1-MM8-025 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM8-025 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM8-025 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM8-025?

No — calculators are banned in the TMUA. TMUA-P1-MM8-025 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM8-025?

TMUA-P1-MM8-025 is Paper P1 · Graphs of functions (specification code MM8), level 3. Drill more of the same topic from this page.

TMUA-P1-MM8-025 — Paper P1 · Graphs of functions · Level 3

P1MM8Level 3~150s target

Spec: MM8 · No calculator · ~150s

What is the horizontal asymptote of

y = \frac{x+1}{x-1}

Options

$y = 0$
$x = 1$ only, no horizontal asymptote
$y = 1$
$y = -1$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: asymptotes, rational-graphs. Name the trap first, work the stem by hand, then open the solution below.

Show solution

x \to \pm\infty

\frac{x+1}{x-1} \to 1

, so the horizontal asymptote is

y = 1

and the correct is C. Trap:

x = 1

is the vertical asymptote, not the horizontal one.

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Same topic · same level

P1MM8Level 3

TMUA-P1-MM8-009

Which statement correctly describes the stationary points of y = x^3 - 3x^2?

Graphs of functions

Open TMUA-P1-MM8-009 →

Same trap: asymptotes

P1MM8Level 2

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What is the vertical asymptote of y = 1/x-2?

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Open TMUA-P1-MM8-018 →

TMUA-P1-MM8-025 — Paper P1 · Graphs of functions · Level 3

Options

Keep practising

Master Graphs of functions

TMUA-P1-MM8-025 — Paper P1 · Graphs of functions · Level 3

Options

Keep practising

Master Graphs of functions