Zadanie 11a
State d.
Higher rational graphs and asymptotes
Analyse rational functions with quadratic terms, including intercepts and vertical, horizontal or oblique asymptotes.
Tę umiejętność sprawdza 26 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 26 Otwórz w wyszukiwarce z filtrami
Zadanie 11b
Show that b=7.
Zadanie 11c
Find c.
Zadanie 11d
Sketch y=f(x) for −25≤x≤25, labelling asymptotes, axis intercepts and local extrema.
Zadanie 12b
Now instead suppose f has a vertical asymptote, oblique asymptote y=x−5, and at least one point of zero gradient. State its vertical asymptote.
Zadanie 12c
Now instead suppose f has a vertical asymptote, oblique asymptote y=x−5, and at least one point of zero gradient. Show that a=−3.
Zadanie 12d
Now instead suppose f has a vertical asymptote, oblique asymptote y=x−5, and at least one point of zero gradient. Show that b ≥ −9.
Zadanie 12e
For a=−3 and b=1: (i) sketch y = f(∣x∣), marking all asymptote equations, its vertical-axis intercept, and all local extrema; (ii) solve f(∣x∣) < f(x).
Zadanie 1d
(i) Prove the identity . (ii) Hence give the equation of its oblique asymptote. (iii) Give one point on the curve at which the tangent is parallel to that asymptote.
Zadanie 9
The curve y = (x + 2)/(ax2 + bx + c) has a local minimum at (1,2) and a vertical asymptote x=−1. The real constants a,b,c are nonzero. Find them.
Zadanie 12c
For k=1, state the vertical asymptote.
Zadanie 12d
For k=1, find the oblique asymptote.
Zadanie 12f
For k=1, sketch the curve with both asymptotes and correct approach behaviour. You need not calculate intercepts.
Zadanie 8a
Determine the range of g.
Zadanie 11a
State the vertical asymptote.
Zadanie 11b
Find the x-axis intersection points.
Zadanie 11c
The oblique asymptote is y=ax+b. Find a,b.
Zadanie 11d
Sketch f for −40≤x≤40, showing its asymptotes and axis intersections.
Zadanie 11e
Find the range of f.
Zadanie 11a
State the vertical asymptote.
Zadanie 11b
Find the x-axis intersection points.
Zadanie 11c
The oblique asymptote is y=ax+b. Find a,b.
Zadanie 11d
Sketch f for −40≤x≤40, showing its asymptotes and axis intersections.
Zadanie 11e
Find the range of f.
Zadanie 11a
Sketch y=f(x), labelling all asymptotes, local extrema and axis intercepts.
Zadanie 11b
(i) Show that . (ii) State its domain.