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Mathematics for IGCSE & O level - Sketching Curves (Section 2)

1
For what x-values does the graph of y = x³ increase?
Answer
(C)
For all x
2
Which of the following equations represents a linear graph?
Answer
(B)
y = 2x + 3
3
If a quadratic graph has a turning point at (1, 2) and opens downwards, what can you conclude about its maximum value?
Answer
(B)
The maximum value is 2.
4
If a graph has an asymptote at y=2, which value will the y-value approach?
Answer
(C)
2
5
In a linear equation, what does the y-intercept represent?
Answer
(C)
The point where the line crosses the y-axis
6
In the context of sketching curves, why is it important to know the x and y intercepts?
Answer
(B)
They help locate the graph on the axes.
7
What information is needed to sketch the graph of y = 1/x + 4? (Select all that apply)
Answer
A
B
D
8
What are the x-intercepts of the graph of y = x² - 2x - 3?
Answer
(A)
-1, 3
9
If the equation of a graph is y=1/x - 3, what is the horizontal asymptote?
Answer
(D)
y=-3
10
Which transformations affect the position of the y-intercept on a function? (Select all that apply)
Answer
B
C
D
11
What do you need to sketch the graph of a quadratic function? (Select all that apply)
Answer
A
B
C
12
What happens to the graph of y = 2^x if you subtract 4?
Answer
(C)
It moves down 4 units.
13
If a linear equation has a slope of -1/2, what does that mean about the graph?
Answer
(B)
The line slopes downwards from left to right.
14
When sketching y=2^(x-1)+4, which of the following are needed? (Select all that apply)
Answer
A
B
C
15
What type of graph is represented by the function y = 1/x?
Answer
(D)
Reciprocal
16
Which of the following is the horizontal asymptote of y = 2^(x-1) + 4?
Answer
(C)
y=4
17
What is the shape of the graph of y = x³ - 1?
Answer
(C)
A cubic curve
18
Which of the following is MOST crucial to sketch the graph of a function?
Answer
(C)
The y-intercept
19
What is the equation of the line of symmetry for the graph of y = x² - 4x + 3?
Answer
(B)
x = 2
20
What is true about the graph of y = -2x² - 4x + 1? (Select all that apply)
Answer
A
B
D
21
What is an asymptote?
Answer
(B)
A line that the graph never touches.
22
What is the horizontal asymptote of the graph y = 3 * 2^x - 5?
Answer
(B)
y = -5
23
What does 'a' represent in the reciprocal graph y = a/x?
Answer
(C)
A constant
24
What is the axis of symmetry for the equation y = x² - 8x + 16?
Answer
(B)
x = 4
25
Which of the following transformations affect the y-intercept of a quadratic graph? (Select all that apply)
Answer
B
C
D
26
What happens to the graph of y = 1/x if you add 3 to the x term?
Answer
(D)
It shifts right by 3 units.
27
What does the asymptote do on the graph y=a^x?
Answer
(C)
It defines a lower or upper bound.
28
What does the line of symmetry pass through in a quadratic graph?
Answer
(C)
The turning point.
29
If the coefficient of the x² term is positive in the quadratic equation, what shape does the graph have?
Answer
(B)
A 'U' shape
30
The function y = -x² + 4 describes a downward-opening parabola. What can we say about its turning point?
Answer
(B)
It is a maximum
31
What is true about the graph y= a^x where a>1?
Answer
(C)
The graph increases as x increases.
32
Which are the characteristics of an exponential function? (Select all that apply)
Answer
B
C
D
33
What transformation occurs when you replace x with -x in a function?
Answer
(C)
Reflection across the y-axis
34
Which of the following are key features to determine for sketching any graph?
Answer
(D)
All of the above
35
In the exponential graph y = a^x, what is the y-intercept, assuming a is a positive number?
Answer
(B)
1
36
What is the x-intercept of the graph of 2x + 3y = 6?
Answer
(C)
3
37
What is important when sketching exponential graphs? (Select all that apply)
Answer
A
B
C
38
What is the y-intercept of the graph of y = 2^x - 8?
Answer
(B)
-7
39
Which of the following is NOT a characteristic of an exponential graph?
Answer
(D)
It has a turning point.
40
Which of the following transformations will affect the vertical asymptote of a reciprocal graph (Select all that apply)
Answer
(B)
Horizontal shift
41
Which statements are helpful when sketching an exponential graph? (Select all that apply)
Answer
A
C
D
42
When working with graphs, why is it important to be able to determine where the graph crosses the x and y axes? (Select all that apply)
Answer
B
C
D
43
What is the axis of symmetry for y = x² + 6x + 5?
Answer
(B)
x=-3
44
Where is the y-intercept for y = 2^x - 8 located?
Answer
(B)
(0, -7)
45
The horizontal asymptote of y = 2^(x+3) + 1 is at
Answer
(C)
y=1
46
Which properties are important for understanding and sketching a function? (Select all that apply)
Answer
A
B
C
D
47
Which of the following transformations would change the x-intercepts of a quadratic graph? (Select all that apply)
Answer
B
C
D
48
What do we need to know when sketching a cubic function? (Select all that apply)
Answer
A
C
D
49
Which of the following equations does NOT represent a function?
Answer
(D)
x² + y² = 1
50
If the graph of y = 1/x is shifted to the right by 2 units, what is the new equation?
Answer
(D)
y = 1/(x - 2)