Cubic, reciprocal, exponential and circle graphs

Học bằng cách chơi

Trả lời những câu hỏi này để kiếm năng lượng, rồi câu cá và khám phá. Không cần tài khoản.

Dành cho nhà giáo dục: slide bài học, ghi chú ôn tập sẵn dùng cho Cubic, reciprocal, exponential and circle graphs (Mathematics, Algebra) — dùng trong bài giảng của bạn, hoặc chạy chủ đề như một hoạt động lớp học tương tác để người học chơi như một trò chơi trực tiếp.

Ghi chú bài học Slide Câu hỏi luyện tập

Ghi chú bài học

Cubic graphs

A cubic has equation y = ax³ + bx² + cx + d with a ≠ 0. The simplest, y = x³, passes through the origin and has rotational symmetry.
A cubic with positive x³ rises from bottom-left to top-right; with negative x³ it falls. It can cross the x-axis up to three times.

Reciprocal graphs

For k ≠ 0, y = k/x is a hyperbola with two separate branches. It is undefined at x = 0.
It never touches the axes: the axes are asymptotes. x = 0 is undefined.
The graph is symmetrical about the lines y = x and y = -x.

Cubic and reciprocal curves

Exponential graphs

y = a^x (with a > 0, a \neq 1) grows or decays rapidly. y = 2^x passes through (0, 1) because 2⁰ = 1.
For a > 1 the graph rises ever more steeply; for 0 < a < 1 (e.g. y = (\frac{1}{2})^x) it decays towards the x-axis, which is an asymptote.
Never negative: y > 0 for all x.

Exponential growth

Circle graphs

A circle with centre the origin and radius r has equation x² + y² = r². For x² + y² = 25, the radius is 5.
To check if a point lies on the circle, substitute it: (3, 4) gives 9 + 16 = 25, so it does.
The tangent to a circle is perpendicular to the radius at the point of contact.

x² + y² = 25

Recognising graphs

Link the shape to the equation: line, parabola, cubic S-shape, hyperbola, exponential curve, circle.

Slide

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Câu hỏi luyện tập

Xem trước miễn phí — 8 trên 35 câu hỏi. Đăng ký để xem tất cả.

1.What is the shape of the graph of y = \frac{1}{x} called?
Easy
- Aparabola
- Bhyperbola
- Cellipse
- Dcubic
2.What is y when x = 0 on y = 2^x?
Easy
- A0
- B1
- C2
- Dundefined
3.What is y when x = 3 on y = 2^x?
Easy
- A6
- B8
- C9
- D5
4.What is y when x = 2 on y = x³?
Easy
- A6
- B8
- C9
- D5
5.What is y when x = -2 on y = x³?
Easy
- A8
- B-8
- C6
- D-6
6.What is y when x = 4 on y = \frac{1}{x}?
Easy
- A4
- B0.25
- C0.4
- D-4
7.What is y when x = -2 on y = \frac{6}{x}?
Easy
- A3
- B-3
- C12
- D-12
8.Which value of x can't be used in y = \frac{1}{x}?
Easy
- A1
- B0
- C-1
- D10

Thêm câu hỏi

9.What does the graph of y = 2^x approach as x becomes very negative?
Easy
- Ay = 1
- By = 0
- Cy = -1
- Dy becomes large
10.What is the radius of x² + y² = 49?
Easy
- A7
- B49
- C24.5
- D14
11.What is the radius of x² + y² = 10?
Easy
- A5
- B\√{10}
- C10
- D100
12.Which point lies on x² + y² = 25?
Medium
- A(3, 4)
- B(4, 4)
- C(5, 5)
- D(2, 3)
13.Which point lies on x² + y² = 13?
Medium
- A(2, 3)
- B(3, 3)
- C(1, 4)
- D(3, 4)
14.Which equation gives a circle of radius 6 centred at the origin?
Medium
- Ax² + y² = 6
- Bx² + y² = 12
- Cx² + y² = 36
- Dx + y = 6
15.Which equation matches a graph that passes through (0, 1) and rises steeply?
Medium
- Ay = 3^x
- By = x³
- Cy = \frac{1}{x}
- Dy = x²
16.Which graph is symmetrical about the origin (rotational symmetry) and S-shaped?
Medium
- Ay = x²
- By = x³
- Cy = 2^x
- Dy = |x|
17.Which graph has the x-axis as an asymptote?
Medium
- Ay = x³
- By = 2^x
- Cy = x²
- Dy = 2x
18.What is y when x = -1 on y = 2^x?
Medium
- A-2
- B0.5
- C-0.5
- D2
19.The curve y = 10 \times 2^x passes through (0, k). What is k?
Medium
- A1
- B10
- C20
- D0
20.A tangent touches the circle x² + y² = 25 at (3, 4). What is the gradient of the radius to that point?
Medium
- A\frac{4}{3}
- B\frac{3}{4}
- C-\frac{3}{4}
- D-\frac{4}{3}
21.The tangent at (3, 4) to x² + y² = 25 has gradient:
Medium
- A\frac{4}{3}
- B\frac{3}{4}
- C-\frac{3}{4}
- D-\frac{4}{3}
22.The graph y = \frac{1}{x} lies in which quadrants?
Easy
- A1st and 2nd
- B1st and 3rd
- C2nd and 4th
- D3rd and 4th
23.Which table gives y = x³ for x = -1, 0, 1?
Easy
- A-1, 0, 1
- B1, 0, 1
- C-3, 0, 3
- D1, 0, -1
24.For y = \frac{1}{x}, what happens to y as x increases from 1 to 100?
Medium
- Ay increases
- By decreases towards 0
- Cy stays the same
- Dy becomes negative
25.Which has no x-intercept?
Medium
- Ay = x³
- By = 2^x
- Cy = x²
- Dy = x - 1
26.What is the centre of the circle x² + y² = 9?
Easy
- A(3, 3)
- B(0, 0)
- C(9, 0)
- D(0, 9)
27.y = x³ passes through the origin.
Easy
True or false?
28.The graph of y = 2^x can be negative.
Easy
True or false?
29.x² + y² = 25 is the equation of a circle of radius 5 centred at the origin.
Easy
True or false?
30.The graph of y = \frac{1}{x} crosses the y-axis.
Easy
True or false?
31.The point (4, 4) lies on x² + y² = 25.
Easy
True or false?
32.The tangent to a circle is perpendicular to the radius at the point of contact.
Medium
True or false?
33.Which graphs pass through (0, 1)?
Medium
- Ay = 2^x
- By = x² + 1
- Cy = \frac{1}{x}
- Dy = x³
- Ey = 5^x
34.Which points lie on x² + y² = 25?
Medium
- A(5, 0)
- B(0, -5)
- C(3, 4)
- D(4, 4)
- E(2, 5)
35.Describe the graph of y = 2^x.
Medium

Unlock all 35 questions & more

Tạo tài khoản miễn phí để xem mọi câu hỏi, slide, thẻ ghi nhớ và ghi chú ôn tập cho chủ đề này.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Đề thi cũ

Luyện đề thi cũ cho chủ đề này sắp ra mắt.

Sắp ra mắt