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Mathematics for IGCSE & O level - Graphs Of Functions (Section 2)

1
What is the shape of the graph when graphed with the function y=1/x?
Answer
(B)
Hyperbola
2
The graph of a quadratic function has a maximum value when which of the following is true about the leading coefficient?
Answer
(B)
It is negative.
3
If the equation of a curve is y = 1 / (x - 2), what is the vertical asymptote?
Answer
(C)
x = 2
4
What best describes the graph of y = ax³, where a > 0?
Answer
(C)
An S-shaped curve increasing from left to right.
5
What characterizes the graph of a function that is symmetrical about the origin?
Answer
(B)
It is an odd function
6
What is the general form of the equation of a straight line?
Answer
(C)
y = mx + c
7
Which of the following are characteristics of the graph of the function y = 1/x?
Answer
A
B
D
8
When the discriminant (b²-4ac) is zero, what does this indicate about the roots of the quadratic equation?
Answer
(B)
One real root (a repeated root)
9
If the equation of a graph is y = -2x + 4, what is the slope of the line?
Answer
(A)
-2
10
What should always be made when drawing a graph?
Answer
(C)
A table of values
11
In a graph, the y-intercept is defined as the point where the curve intersects which axis?
Answer
(B)
y-axis
12
Which of the following is an example of a reciprocal graph?
Answer
(B)
y = 1/x
13
Which of the following statements is true regarding the roots of a quadratic equation?
Answer
B
C
14
The solution(s) to the equation x² - 3x - 8 = 0 are represented by what when using a graph?
Answer
(A)
The x-intercepts of the graph of the equation.
15
Which of the following describes the x-coordinate of the vertex of the quadratic equation y = ax² + bx + c?
Answer
(A)
-b / 2a
16
For the equation y = -x² + 4, what is the vertex of the parabola?
Answer
(B)
(0, 4)
17
Which of the following is a key point when drawing a graph?
Answer
(C)
Draw a smooth curve
18
What is the x-coordinate of the vertex of the parabola y = -x² + 4x - 3?
Answer
(C)
2
19
What is the graphical representation of a cubic function called?
Answer
(C)
Cubic curve
20
Which function below does not have a real-number y-value when x = 0?
Answer
(C)
y = 1/x
21
When solving a quadratic equation graphically, how is the solution(s) found?
Answer
(B)
The x-intercepts of the graph
22
What is the shape of the graph of the equation y = x² - 4?
Answer
(B)
Parabola
23
In the formula for Zari's car value, V = 5000 * 0.85^t, what does 0.85 represent?
Answer
(B)
The rate of depreciation
24
What is the domain of the function y = x² - 4x + 3?
Answer
(B)
All real numbers
25
Which of the following are correct concerning the graph of y = x² - 4x + 4?
Answer
A
B
26
What does the term 'root' refer to when discussing a quadratic or cubic graph?
Answer
(B)
The point where the graph touches the x-axis
27
What is the degree of the function y = x³ - 2x + 1?
Answer
(C)
3
28
What is the value of the discriminant (b² - 4ac) if a quadratic equation has two distinct real roots?
Answer
(B)
Greater than zero
29
What is the key to estimating the gradient of a curve at a point?
Answer
(C)
Draw a tangent at that point
30
What does the constant 'c' represent in the quadratic equation y = ax² + bx + c?
Answer
(B)
The y-intercept
31
What is the y-value of the function y = 2x² - 8 when x = 2?
Answer
(A)
0
32
What type of graph does not have a y-intercept?
Answer
(D)
Cubic function
33
In the linear equation y = -x + 7, what is the y-intercept?
Answer
(A)
7
34
If a quadratic function's graph touches the x-axis at only one point, what does this signify about the roots?
Answer
(B)
One real root (a repeated root)
35
Which features of the graph change when the 'c' value changes in y = ax² + bx + c?
Answer
(A)
The y-intercept
36
What is the y-intercept of the graph of y = x² + 2x - 3?
Answer
(A)
-3
37
For the equation y = x² - 6x + 9, what is the x-coordinate of the vertex?
Answer
(B)
3
38
What does the vertex of a parabola represent in the context of the equation's solutions?
Answer
(B)
The minimum or maximum point of the curve
39
If the graph of a cubic function has three real roots, how many times does it intersect the x-axis?
Answer
(D)
3
40
If a quadratic equation has one real root, how does its graph interact with the x-axis?
Answer
(C)
It touches the x-axis at one point.
41
The graph of y=x²+2x-8 crosses the x axis at:
Answer
A
B
42
What is the range of the function y = 1/x when x > 0?
Answer
(A)
y > 0
43
When graphing the function y = x² - 4x + 3, what is the y-value when x = 0?
Answer
(B)
3
44
What do you call the point where a graph of y=x³ changes its concavity?
Answer
(B)
The point of inflection
45
In the context of exponential graphs, what does 'a' represent if a > 1?
Answer
(B)
Growth
46
What do the solutions of a quadratic equation represent graphically?
Answer
(B)
The x-intercepts
47
What type of function can never touch the x-axis?
Answer
(D)
Reciprocal
48
What is the general form of a rational function?
Answer
(C)
y = P(x) / Q(x)
49
If the roots of a quadratic equation are real and equal, what does the graph of the equation look like?
Answer
(C)
It touches the x-axis at one point.
50
What is the significance of the roots of an equation as they relate to its graph?
Answer
(B)
The x-intercepts of the graph