Zadanie 4b
The same height is written as . Find the least positive integer d.
Basic graph transformations
Apply translations, reflections and stretches, tracking their order and the movement of points and features.
Tę umiejętność sprawdza 16 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 16 Otwórz w wyszukiwarce z filtrami
Zadanie 7c
Let g(x) = x − 5. (i) Describe the transformation from y=f(x) to y = (g∘f)(x). (ii) Hence state the range of g∘f.
Zadanie 3c
Find the range of g.
Zadanie 9b
(i) Find g−1(x). (ii) Describe a sequence of transformations taking the graph of g−1 to the graph of f.
Zadanie 1
The top diagram defines f on −2≤x≤2 by connected straight segments, including both endpoints. Match each expression to one of graphs A–F: (i) y = f(x − 1); (ii) y = f(x) + 1; (iii) y = f(−x); (iv) y = f(3x). Each graph uses the displayed scale.
- Materiał graficzny
Zadanie 5c
Write g in the form p sin[b(x−q)]+2, with p,q positive integers. (i) Find the smallest positive q. (ii) State p for that q.
Zadanie 5b
Describe a sequence of transformations taking y = 1/x to y = f(x).
Zadanie 7c
State (i) g(x); (ii) the domain of g.
Zadanie 7d
It is found that g(t) = (2/3)f(t) + q. Find q.
- Materiał graficzny
Zadanie 8d
For x>0, obtain the graph of y = f(3x2) from y = log3 x using one translation and one stretch. Describe both transformations and their order.
Zadanie 8d
For x>0, obtain the graph of y = f(125x3) from y = log5 x using one translation and one stretch. Describe both transformations and their order.
Zadanie 6b
Sketch g on 0≤x≤8m, labelling its zeros and extrema.
- Materiał graficzny
Zadanie 3b
A horizontal stretch by factor k, followed by a vertical translation by c, transforms f into g. Find k,c.
Zadanie 3b
A horizontal stretch by factor k, followed by a vertical translation by c, transforms f into g. Find k,c.
Zadanie 6a
Describe two transformations taking the graph of f to the graph of g.
Zadanie 8b
(i) Find the inverse function. (ii) Prove algebraically that reflecting the graph of f in the y-axis and then in the x-axis produces the graph of its inverse.