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Mathematics for IGCSE & O level - Sketching Curves (Section 1)

1
What is the slope of the line 2x + 3y = 12?
Answer
(B)
-2/3
2
To sketch a graph of a polynomial function, what information is generally useful? (Select all that apply)
Answer
A
B
C
3
Which of the following are true about the graph of y = 2^x? (Select all that apply)
Answer
A
B
C
4
What information is crucial for sketching reciprocal graphs? (Select all that apply)
Answer
A
B
C
5
Which information is crucial for sketching a function in general? (Select all that apply)
Answer
A
B
C
6
What is the vertical asymptote of the graph of y = 1/x + 2?
Answer
(A)
x = 0
7
What is the first step in sketching the graph of y = x² + 5x + 6?
Answer
(D)
Identify the shape.
8
Which statement describes the key feature for determining the horizontal asymptote of y=1/(x+2) + 3?
Answer
(C)
As x approaches infinity, y approaches 3.
9
Which of the following can represent a quadratic graph? (Select all that apply)
Answer
B
C
10
Which of the following transformations, or combinations thereof, could change the x-intercept(s) of an exponential graph? (Select all that apply)
Answer
A
B
C
11
What is the shape of the graph of y= a^x, where a is a positive integer?
Answer
(C)
An exponential curve
12
Which statement is true for a cubic function of the form y = ax³ when a is positive?
Answer
(C)
The graph increases as x increases.
13
If an exponential function is of the form y = a^(x) where 0 < a < 1, what can you conclude about its graph?
Answer
(C)
The graph decreases.
14
What are the x-intercept(s) of the graph y = x² - 4?
Answer
(C)
2, -2
15
Which key pieces of information are needed to sketch the graph of an exponential function? (Select all that apply)
Answer
A
B
C
16
The x-intercepts of the graph of y = (x + 3)(x - 1) are:
Answer
(A)
-3, 1
17
In an exponential function, y=a^x, If a=1/2, what is the graph like?
Answer
(C)
Exponential decay
18
If y = x² - 6x + 9, what is the turning point of the graph?
Answer
(A)
(3, 0)
19
What is the value of y when x = 0 in the equation 2x - 3y = 12?
Answer
(B)
-4
20
What does the 'a' value determine in the quadratic graph y = ax² + bx + c?
Answer
(C)
The direction of opening.
21
Which of the following are helpful when sketching a reciprocal graph? (Select all that apply)
Answer
A
B
C
22
Which of the following statements are true about the general cubic function (Select all that apply)
Answer
A
C
23
In an exponential function, what does the base number influence?
Answer
(C)
The rate of growth or decay.
24
What is the horizontal asymptote of y = 2^(x+1) - 3?
Answer
(B)
y = -3
25
What is the vertical asymptote of y = 1/(x+2) - 1?
Answer
(B)
x = -2
26
Which of the following is a characteristic of the graph of y = 1/x + 2?
Answer
A
B
27
Which of the following are characteristics of a quadratic graph? (Select all that apply)
Answer
A
B
D
28
Which features are present in the graph of y=a/x when a is negative? (Select all that apply)
Answer
A
C
D
29
What is the x-intercept(s) of the graph y = (x-1)(x+2)?
Answer
(A)
1, -2
30
The turning point on a quadratic graph is also known as:
Answer
(B)
The vertex.
31
For what values of x is the graph of y = x³ - 8 increasing?
Answer
(C)
for all values of x
32
Which features are associated with reciprocal graphs? (Select all that apply)
Answer
A
B
33
Which of the following is the graph of a function which does *not* cross the x-axis?
Answer
(B)
y = x² + 1
34
What is the equation of a hyperbola that has a horizontal asymptote at y=3?
Answer
(A)
y = 1/x + 3
35
What are the asymptotes for the graph y = 1/(x+3) + 2?
Answer
(B)
x = -3, y = 2
36
What is the shape of a quadratic graph when the coefficient of x² is positive?
Answer
(D)
A 'u' shape.
37
To sketch a graph of the form y = ax² + bx + c, which of the following are helpful to identify? (Select all that apply)
Answer
A
B
D
38
Which statement is true regarding the graph of y = x³?
Answer
(C)
It's symmetrical about the origin.
39
If the coefficient of x² in a quadratic equation is negative, what does that indicate about the graph?
Answer
(C)
The graph opens downwards.
40
How many x-intercepts can a quadratic graph have?
Answer
(B)
Zero, one, or two
41
What is the horizontal asymptote of the graph of y = 1/x + 4?
Answer
(D)
y=4
42
Which of the following is a key step in sketching a graph of a function?
Answer
(A)
Finding where the graph crosses the y-axis.
43
What happens to the graph of y = 1/x if you multiply the whole equation by -1?
Answer
(B)
It reflects across the x-axis.
44
What information is useful when sketching cubic graphs? (Select all that apply)
Answer
A
C
D
45
Which transformation is represented by the function y = f(x - 2)?
Answer
(B)
A horizontal shift right by 2 units
46
For cubic functions, what information is most helpful when sketching the graph? (Select all that apply)
Answer
A
B
D
47
Which of the following is a characteristic of a linear graph?
Answer
(C)
It is a straight line.
48
If the line 3x + 4y = 12 is graphed, what is the y-intercept?
Answer
(B)
4
49
The graph of y = -x² + 4 will intersect the y-axis at:
Answer
(C)
4
50
In the equation y = a^x, which factor changes the y-intercept?
Answer
(D)
Any constant added or subtracted to the whole function