Zadanie 1a
For A = 9: (i) Sketch y = F9(x) on −7 ≤ x ≤ 7. (ii) State all its intersections with the horizontal axis. (iii) State the local maximum and local minimum coordinates.
Representing functions graphically
Draw or sketch functions with appropriate labelled features and use graphing tools to represent defined relationships.
Tę umiejętność sprawdza 27 zadań wzorowanych na arkuszach IB z lat 2022–2025.
Zadania sprawdzające tę umiejętność: 27 Otwórz w wyszukiwarce z filtrami
Zadanie 6a
(i) Rewrite f(x) using only sine and cosine. (ii) Sketch its graph on the given domain and label its horizontal intercept.
Zadanie 10b
Sketch y = f(x). Label the vertex and every intercept with a coordinate axis.
Zadanie 12c
Sketch the particular solution through (−3, 2) for −4 ≤ x ≤ 4, labelling the coordinates of its local maximum and minimum.
Zadanie 1d
On one pair of axes sketch (i) H; (ii) its two distinct normals passing through (0,1). Mark each point of normal contact. Exact contact coordinates and line equations are not required.
Zadanie 1c
Sketch y=f(x) on its full domain, labelling the intercepts, endpoints and maximum.
Zadanie 1a
Sketch f_1, stating the coordinates of its local maximum.
Zadanie 1a
On common axes, sketch y = log2 x, y = log10 x and y = x2 + e2 for x>0. Label all three graphs and state the nonzero x-intercept.
Zadanie 1d
Investigate representative graphs. State the number of intersections in each base range: (i) 0<a<1; (ii) 1<a<1.05; (iii) 1.1<a<2.
Zadanie 2b
Sketch y=(f∘g)(x) for −0.55≤x≤0.55, labelling local extrema.
Zadanie 2b
For a=4 and b=√5, sketch x2/25 + y2/16 = 1 and x2/4 − y2/5 = 1 on common axes. Label each curve and its x-intercepts. Intersection coordinates are not required.
Zadanie 2a
Sketch f for −3≤x≤3.
Zadanie 2a
Sketch f for −3≤x≤3.
Zadanie 9a
Show that f is even.
Zadanie 9a
Show that f is even.
Zadanie 11c
Sketch F on 0 ≤ x ≤ π/2. The endpoint maxima have height e+1 and second derivative −16(e+1); the middle minimum at π/4 has height e⁻¹−1 and second derivative 16(1+e⁻¹). Reflect these curvature sizes in the sketch.
Zadanie 11d
Sketch f for −40≤x≤40, showing its asymptotes and axis intersections.
Zadanie 11c
Sketch F on 0 ≤ x ≤ π/2. The endpoint maxima have height e+1 and second derivative −16(e+1); the middle minimum at π/4 has height e⁻¹−1 and second derivative 16(1+e⁻¹). Reflect these curvature sizes in the sketch.
Zadanie 11d
Sketch f for −40≤x≤40, showing its asymptotes and axis intersections.
Zadanie 1a
On the same axes, sketch (i) C₁ and (ii) C₂ in the window −2≤x≤5,−5≤y≤5. Mark their intersections with the coordinate axes.
Zadanie 1b
(i) State the coordinates of C₂’s two inflection points. (ii) Identify two features that distinguish C₁ from C₂.
Zadanie 1c
Vary the positive integer b in y2 = (x − 1)3 + b. Suggest two features shared by every curve in this family.
Zadanie 2c
Sketch y=f(x) and its tangent at A, marking the tangent’s x-intercept.
Zadanie 2h
Let g(x) = (x − r)2[(x − a)2 + b2], b>0, with A=(a,g(a)) and R=(r,0). When a≠r the tangent at A has x-intercept T=((a+r)/2,0). (i) Sketch the curve for a=r=−1 and b=2. (ii) For general a=r, state the coordinates of A and of the curve’s minimum point.
Zadanie 10a
Sketch y=f(x), labelling both endpoints.
Zadanie 2a
Find the coordinates of A.
Zadanie 11b
Suppose x2 − 3x + 2 is a factor of P. (i) Express b in terms of a. (ii) Hence show that a=5,b=8,c=4 is the only permitted assignment. (iii) Factor P completely into linear factors. (iv) Sketch y=P(x), labelling all intercepts.