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