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Mathematics for IGCSE & O level - Sketching Curves (Section 5)

1
How many x-intercepts does the graph of \(y = x^2 + 4\) have?
Answer
(A)
0
2
How many asymptotes does the graph of \(y = \frac{1}{x-2} + 3\) have?
Answer
(C)
2
3
Which of the following methods could be used to sketch a quadratic graph?
Answer
A
B
C
4
In the equation \(y = \frac{a}{x}\), where does the graph not meet the axes?
Answer
(C)
Both axes.
5
Which value determines whether a parabola opens upwards or downwards?
Answer
(B)
The sign of the coefficient of x^2
6
Which of the following statements about the graph of \(y=x^3\) is correct?
Answer
(B)
The graph passes through (0,0) and (1,1).
7
When sketching a graph, which features are most important to include?
Answer
B
C
8
Which feature is essential to indicate on a graph?
Answer
A
B
9
Which of the following describes the behavior of \(y = \frac{1}{x}\) as \(x\) approaches infinity?
Answer
(C)
y approaches 0
10
What is the main purpose of sketching a graph?
Answer
(B)
To visually represent the relationship between variables.
11
What does 'a' determine in a graph of \(y = a^x\)?
Answer
(C)
The base of the exponent, and growth/decay
12
What happens when a positive constant is added to the entire equation of an exponential graph?
Answer
(B)
Vertical translation up
13
For a function of the form \(y = a^x\), what does the y-intercept always equal?
Answer
(B)
1
14
How many x-intercepts can a quadratic function have?
Answer
(A)
0, 1, or 2
15
In an exponential function \(y = a^x\), which factor affects the x-intercept?
Answer
(C)
Neither
16
What is a key feature of a reciprocal graph?
Answer
A
C
17
If you are sketching a graph, which of the following is the MOST important step?
Answer
(B)
Drawing the correct shape for the type of graph.
18
Which of the following can be determined by looking at a completed square form of a quadratic equation?
Answer
B
C
19
What happens to the graph of \(y = 2^x\) if the equation becomes \(y = 2^x - 4\)?
Answer
(C)
The graph shifts 4 units downwards.
20
If the function is \(y=x^3+x^2-6x\), how can you find where this graph crosses the x-axis?
Answer
(A)
Set y = 0 and solve for x
21
What is the equation of the line of symmetry for the graph of \(y = x^2 - 6x + 10\) after it has been rewritten in completed square form?
Answer
(B)
x = 3
22
Which of these options is correct about a quadratic function?
Answer
(B)
A quadratic function forms a parabola.
23
Which of the following statements is TRUE about the graph of an exponential function?
Answer
(B)
It always passes through the point (0, 1).
24
What is the main reason for rewriting a quadratic function in completed square form?
Answer
(C)
To identify the vertex (turning point).
25
What information is required to accurately sketch a linear graph?
Answer
(A)
The slope and y-intercept