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Mathematics for IGCSE & O level - Graphs Of Functions (Section 1)

1
Which type of symmetry does the graph of a reciprocal function (y = 1/x) exhibit?
Answer
(C)
Symmetry about the origin
2
What is the maximum number of turning points a cubic graph can have?
Answer
(B)
1
3
What kind of function is the equation y = x³ - 3x?
Answer
(C)
Cubic
4
How do you find the roots of the function y = x² - 4x + 3?
Answer
(A)
Set y = 0 and solve for x.
5
In a linear equation, what does the slope represent?
Answer
(C)
The rate of change
6
For a quadratic function to have only one real root, which of the following is true?
Answer
(B)
The vertex lies on the x-axis.
7
Which are the key elements when drawing a graph? (checkbox)
Answer
A
B
C
8
How can equations be solved?
Answer
(A)
By looking at the graph
9
If you are given the roots of a quadratic equation, and you want to sketch the graph, which information helps you find the y-intercept?
Answer
(B)
The value of a.
10
How many asymptotes does the graph of y = 1/x have?
Answer
(C)
2
11
What is the shape of the graph that represents a cubic function of the form y = ax³ + bx² + cx + d?
Answer
(D)
S-shaped curve
12
What can be said about the graph of a function if the function is odd?
Answer
(C)
It has symmetry about the origin
13
What can be determined about the value of 'a' in the function y = ax² + bx + c if the parabola opens downwards?
Answer
(B)
a < 0
14
What are the key points needed to graph a parabola?
Answer
A
B
D
15
When drawing the graph of y = 1/x, as x gets very large (approaches infinity), what does y approach?
Answer
(A)
0
16
What does the y-coordinate of the vertex of a parabola represent?
Answer
(C)
The maximum or minimum value of the function
17
Which of the following describes the shape of the graph of y=x³?
Answer
(B)
An S-shaped curve
18
If the coefficient of x³ in a cubic graph is negative, the graph will:
Answer
(A)
Start from top left and go to bottom right
19
Which term determines the number of real roots a quadratic equation has?
Answer
(B)
The discriminant
20
If the x-axis is an asymptote of a graph, what is the value that the function approaches as x goes to infinity or negative infinity?
Answer
(A)
0
21
What is the maximum number of real roots a quadratic equation can have?
Answer
(C)
2
22
In the graph of a rational function, the horizontal asymptote represents:
Answer
(B)
The value that the function approaches as x approaches infinity or negative infinity
23
Which feature determines the steepness of a straight-line graph?
Answer
(C)
The slope
24
If the graph of a cubic function crosses the x-axis three times, how many real roots does the function have?
Answer
(D)
3
25
What is the value of y when x = 0 in the equation y = -x² + 5x - 6?
Answer
(A)
-6
26
What is the range of the function y = -x²?
Answer
(B)
y ≤ 0
27
What type of function does not have a defined y-value when x = 0?
Answer
(C)
Reciprocal
28
Which of the following functions has a horizontal asymptote?
Answer
(C)
y = 1/x
29
What can exponential curves be used to represent? (checkbox)
Answer
A
B
30
Which of the following statements are true about the graph of y = 1/x?
Answer
A
B
C
31
Which of the following equations, when graphed, results in a curve with two separate branches?
Answer
(C)
y = 1/x
32
For the function y = x², at what x value is the graph symmetrical?
Answer
(A)
x = 0
33
Which feature of a cubic function is characterized by a change in concavity?
Answer
(C)
Point of inflection
34
The range of y = x² is:
Answer
(B)
y ≥ 0
35
Which statements are true about a parabola?
Answer
A
C
36
What is the shape of the graph of the function y = 2x + 1?
Answer
(B)
Straight line
37
For the graph of y = x² + 2x + 1, where does the graph touch the x-axis?
Answer
(A)
x = -1
38
What is the effect of a 'b' value on the graph of a quadratic equation of the form y = ax² + bx + c?
Answer
(B)
It affects the x-coordinate of the vertex
39
If the slope of a line is 0, what kind of line is it?
Answer
(A)
Horizontal
40
Which of the following are correct regarding the graph of the cubic equation y = x³ - 1?
Answer
A
C
41
If a quadratic equation has no real roots, how does its graph appear?
Answer
(C)
It does not intersect the x-axis.
42
What is a key characteristic of the graph of y = 1/x related to the x and y axes?
Answer
(C)
It never touches either axis.
43
If the graph of a function is symmetrical about the y-axis, which of the following must be true?
Answer
(A)
The function is even.
44
If a graph has a vertical asymptote, what is the value of x at that asymptote?
Answer
(C)
The x value that makes the denominator of the function 0
45
In the parabola equation y = a(x - h)² + k, what do the values (h, k) represent?
Answer
(C)
The vertex of the parabola
46
What is the domain of the function y = 1/x²?
Answer
(B)
All real numbers except x = 0
47
Which graph type is represented by the equation y = x³?
Answer
(C)
Cubic curve
48
How do you solve equations graphically, such as x² - 2x - 3 = 5 ?
Answer
(A)
Draw the line y=5 on the graph of the equation and read the intersections.
49
For the function y = 3x - 2, what is the y value when x = 1?
Answer
(B)
1
50
In the equation of the form y = ax² + bx + c, which term determines the direction in which the parabola opens?
Answer
(A)
a