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Mathematics for IGCSE & O level - Graphs Of Functions (Section 3)

1
Which statement is true about the nature of the solutions (roots) of a quadratic equation if its graph does not intersect the x-axis?
Answer
(C)
The equation has no real roots.
2
What determines the horizontal position of the vertex of a parabola?
Answer
(D)
The 'b' value
3
What would be the shape of the graph of y = 3x - 1/2?
Answer
(B)
Straight Line
4
If the vertex of a parabola is at (1, -2) and the parabola opens upwards, what is the minimum value of the function?
Answer
(B)
-2
5
The general form of a quadratic function is y = ax² + bx + c. When the graph of a quadratic equation is drawn, it produces a curve called:
Answer
(A)
A parabola
6
What is the term used to denote the points where a graph intersects the x-axis?
Answer
(B)
Zeros
7
Which type of graph is typically used to solve quadratic equations?
Answer
(B)
Parabola graphs
8
What is the equation of the axis of symmetry for the parabola represented by y = 2x² - 4x + 1?
Answer
(B)
x = 1
9
The graph of a quadratic equation has a vertex at (2,3). If the parabola opens upwards, then:
Answer
(C)
The equation has two distinct real roots.
10
If the multiplier 'a' in the exponential function y = a*b^x is less than 1, what type of behavior does it represent?
Answer
(B)
Decay
11
What describes the slope of a horizontal line on a graph?
Answer
(C)
Zero
12
What is the general form of an exponential graph?
Answer
(C)
y = ka^x
13
What do you need to know to fully sketch the graph of a quadratic equation?
Answer
A
B
C
14
What is the definition of gradient?
Answer
(A)
Increase in y / Increase in x
15
What is the effect of a negative 'a' value on the graph of y = ax²?
Answer
(B)
The graph opens downwards.
16
In the quadratic equation y = 3x² - 6x + 2, what is the role of the term '-6x'?
Answer
(B)
Affects the horizontal position of the vertex.
17
Which of the following equations are solved by finding the points of intersection of a line and a curve?
Answer
A
D
18
Which of the following is the general form of a cubic graph?
Answer
(C)
y = ax³ + bx² + cx + d
19
What is the value of the y-coordinate when x = 1, for the equation y = x² + 2x?
Answer
(C)
3
20
For the linear equation y = -3x + 5, what is the gradient of the line?
Answer
(B)
-3
21
What does the 'a' value in y = a(x - h)² + k indicate about the parabola?
Answer
(B)
The direction it opens and its width
22
What key point is mentioned regarding reciprocal functions?
Answer
(B)
They have graphs with two separate branches.
23
What is the y-intercept of the graph represented by the equation y = 3x² + 2x - 1?
Answer
(A)
-1
24
What is the range of the function y = (x - 2)² + 3?
Answer
(B)
y ≥ 3
25
Which statement is true about the graph of y = 1/x?
Answer
(A)
The graph has vertical and horizontal asymptotes.
26
In the equation y = (x - 3)² + 1, what is the vertex of the parabola?
Answer
(A)
(3, 1)
27
What are the roots of the quadratic function y = x² - 5x + 6?
Answer
(A)
x=2, x=3
28
The roots of the equation x² - 8 = 0 is/are?
Answer
A
C
29
Which statements are true about the graph of y = -x² + 4x - 3?
Answer
A
B
C
D
30
If a parabola has its vertex on the x-axis, how many real roots does the related quadratic equation have?
Answer
(B)
One
31
Which feature of a graph helps one determine if a function is a quadratic or not?
Answer
(B)
Whether it is a smooth curve and has a U-shape
32
Which of the following would be considered a root of the graph of y = x² - 9?
Answer
(B)
x = 3
33
Which of the following is true about the graph of a linear equation?
Answer
(B)
It is always a straight line.
34
What is the y-intercept of the equation y = 2x² - 4x?
Answer
(A)
0
35
What do you call the curved shape produced when a quadratic equation is graphed?
Answer
(B)
Parabola
36
What is the slope of the line represented by the equation 2y = 4x - 6?
Answer
(B)
2
37
Which is the most suitable way of drawing a tangent line?
Answer
(C)
Try to move your ruler so there is an equal amount of space between the curve and the tangent on each side of the given point.
38
What does a table of values primarily help when graphing a function?
Answer
(C)
To get the ordered pair (x, y).
39
What type of graph does y = x^3 - 3x + 2 likely represent?
Answer
(C)
A cubic curve
40
What is the shape of a reciprocal graph and how many branches does it usually have?
Answer
(C)
Two separate curves, two branches.
41
Which of the following statements is true about the graph of a linear function?
Answer
(C)
The graph is a straight line.
42
If you are using the graph to calculate an equation like 3^x=20, what can you find?
Answer
(A)
x value
43
Which of the following will be observed in a reciprocal graph?
Answer
A
B
44
If a quadratic graph's equation is y = x^2 - 4, where does the curve cut the x-axis?
Answer
A
B
45
In the coffee problem where T = 60 * 0.9^x + 20, what is the temperature of the coffee when Irina makes it?
Answer
(D)
0
46
When plotting the graph for y = 1/x, why is it essential to consider points where x is close to zero?
Answer
(B)
To clearly show the vertical asymptote.
47
Which of the following is a key element when drawing the graph of a quadratic equation?
Answer
(C)
Plotting several points and then connecting them to form a smooth curve.
48
In the equation y = a/x, the graph's branches never touch the axes. What are these axes called?
Answer
(C)
Asymptotes
49
In the given formula for the value of a car, what is the value of the car after zero years?
Answer
(B)
5000
50
What is the relationship between the roots of a quadratic equation and its graph?
Answer
(B)
The roots are the x-intercepts of the graph