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Mathematics for IGCSE & O level - Sketching Curves (Section 3)

1
Which of the following is NOT a key point to consider when sketching any graph?
Answer
(D)
The exact location of all points.
2
What type of symmetry does a parabola exhibit?
Answer
(C)
Line symmetry
3
In the equation y = 2^x, what is the asymptote?
Answer
(B)
y=0
4
Which statement best describes the graph of y=a/x where a < 0?
Answer
(B)
It lies in the second and fourth quadrants.
5
What are the key characteristics of a reciprocal graph (y=a/x)? (Select all that apply)
Answer
A
C
D
6
When sketching graphs, what is essential information to have? (Select all that apply)
Answer
A
B
C
D
7
What is the y-intercept of the graph of y = x² + 4x + 3?
Answer
(B)
3
8
Which of the following is always true for a reciprocal graph? (Select all that apply)
Answer
A
B
D
9
How many asymptotes does a reciprocal graph generally have?
Answer
(C)
Two
10
What key elements should be considered when sketching any function? (Select all that apply)
Answer
A
B
C
11
Where does the graph of y=2^x intersect the y-axis?
Answer
(A)
At (0, 1)
12
Which type of graph has a line of symmetry?
Answer
(B)
Quadratic
13
Which of these statements accurately describe characteristics of quadratic graphs? (Select all that apply)
Answer
A
B
14
Which of these functions would be represented by a curve that is symmetrical?
Answer
(D)
y = x² + 2x - 3
15
What is the y-intercept of y = -x² + 3x + 2?
Answer
(B)
2
16
What is the turning point of the function y = (x - 2)² + 3?
Answer
(A)
(2, 3)
17
What is the gradient of the line 4x - 2y = 8?
Answer
(B)
-2
18
What does completing the square help you find in a quadratic equation?
Answer
(C)
The turning point
19
What is the main advantage of using the completed square form to sketch the quadratic graph? (Select all that apply)
Answer
A
C
D
20
How does adding a constant to the denominator of a fraction of the form \(y= \frac{1}{x}\) affect the asymptotes?
Answer
(A)
The vertical asymptote shifts.
21
In a hyperbola, where are the asymptotes located?
Answer
C
D
22
What is the behavior of an exponential graph \(y = a^x\) where 0 < a < 1?
Answer
(B)
Always decreasing
23
What is the shape of the graph of a quadratic function with a positive coefficient for the \(x^2\) term?
Answer
(B)
A parabola opening upwards
24
What is the effect on the graph of \(y = x^2\) when you change the equation to \(y = (x - 4)^2\)?
Answer
(C)
Shift 4 units right
25
Which is true of \(y = \frac{1}{x-3}\)?
Answer
(B)
It has a vertical asymptote at x = 3.
26
Which of the following will change the location of an asymptote?
Answer
(B)
Adding a constant to the entire equation
27
For a quadratic function, what does the sign of the coefficient of \(x^2\) tell you?
Answer
(C)
The direction the parabola opens
28
What happens to the graph of \(y = 2^x\) if the equation becomes \(y = 2^{x-2}\)?
Answer
(B)
The graph shifts 2 units to the right.
29
Which of the following are true of a graph which decreases across all real numbers?
Answer
A
C
30
What is the y-intercept of the graph of \(y=x^2 - 4\)?
Answer
(B)
-4
31
What does the coefficient of x in the cubic function \(y = x^3\) tell you about the graph?
Answer
(D)
It does not affect the basic shape.
32
What effect does a vertical shift of an exponential function have on its horizontal asymptote?
Answer
(A)
It moves the asymptote upwards.
33
What is the general form of a quadratic equation?
Answer
(B)
y = ax^2 + bx + c
34
Which of the following can be used to sketch the graph of \(y = x^2 + 4x + 3\)?
Answer
A
B
D
35
Which statement is correct regarding the shape of the graph for \(y = 2^x\)?
Answer
(B)
The graph crosses the y-axis at (0, 1).
36
Which of the following is a characteristic of a cubic graph of the form \(y = x^3\)?
Answer
(C)
It passes through the origin
37
In the sketch of \(y=5-x^2\), which is true of the curve?
Answer
(C)
It will cross the y-axis at y=5
38
Which of the following is the key feature of an exponential graph, \(y = a^x\), when 0 < a < 1?
Answer
(D)
The graph decreases as x increases.
39
Which of the following are key elements to include when sketching a graph of any function?
Answer
A
C
40
What is true about the graph of \(y = a^x\) where a is a positive integer, and a > 1?
Answer
A
B
C
41
What happens to the graph of \(y=x^3\) if you reflect it in the x-axis?
Answer
(C)
The graph will be inverted.
42
Which of the following equations describes a graph that does not cross the x-axis?
Answer
(B)
y = x^2 + 1
43
What is a characteristic of the graph of \(y = -x^2\)?
Answer
(B)
The graph is symmetric with respect to the y-axis.
44
What type of graph is described by the equation \(y=ax^2 + bx + c\), where a, b, and c are constants and a != 0?
Answer
(B)
Quadratic
45
If the function is \(y=x^2 + 2x - 3\), find the y-intercept.
Answer
(A)
-3
46
Which of the following statements is TRUE regarding the graph of \(y = -2^x\)?
Answer
(C)
It has a horizontal asymptote at y = 0.
47
Which type of graph has a vertical asymptote?
Answer
(C)
Reciprocal
48
A quadratic function is given as \(y = x^2 - 6x + 10\). Which of the following methods can be used to find the coordinates of its turning point?
Answer
(A)
Completing the square
49
Which of the following describes the characteristics of a graph that increases across all real numbers?
Answer
(C)
An exponential graph with a base greater than 1
50
What happens to the graph of \(y = \frac{1}{x}\) if you change the equation to \(y = \frac{1}{x - 1}\)?
Answer
(C)
The graph shifts 1 unit to the right.