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