Hàm số và Đồ thị Practice Questions
THPT (Vietnam) · THPT Toán · 150 free MCQs with instant results and detailed explanations.
150
Total
45
Easy
77
Medium
28
Hard
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Sample Questions from Hàm số và Đồ thị
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Q1
Easy
If the graph of the function g(x) = 3x - 4 intersects the y-axis, what is the y-coordinate of the intersection point?
A.
-4
B.
4
C.
3
D.
0
Show Answer & Explanation
Correct Answer: A
To find the y-intercept of a linear function, set x = 0. For g(x) = 3x - 4, g(0) = 3(0) - 4 = -4. Thus, the y-coordinate at the intersection with the y-axis is -4.
Q2
Easy
Which of the following is a characteristic of an even function?
A.
f(x) = f(-x) for all x
B.
f(x) = -f(-x) for all x
C.
The graph is symmetric about the x-axis
D.
The graph is symmetric about the origin
Show Answer & Explanation
Correct Answer: A
An even function satisfies the condition f(x) = f(-x) for every x in its domain, which implies that its graph is symmetric about the y-axis.
Q3
Easy
For the quadratic function f(x) = x^2 - 4x + 3, what is the value of f(2)?
A.
1
B.
0
C.
-1
D.
3
Show Answer & Explanation
Correct Answer: A
To find f(2), substitute x = 2 into the function: f(2) = 2^2 - 4(2) + 3 = 4 - 8 + 3 = -1.
Q4
Medium
What is the y-intercept of the linear function f(x) = 3x + 4?
A.
4
B.
3
C.
0
D.
7
Show Answer & Explanation
Correct Answer: A
The y-intercept of a linear function is the value of the function when x = 0. By substituting x = 0 into f(x), we get f(0) = 3(0) + 4 = 4.
Q5
Medium
Determine the vertex of the quadratic function f(x) = x^2 - 4x + 3.
A.
(2, -1)
B.
(1, -2)
C.
(2, -5)
D.
(0, 3)
Show Answer & Explanation
Correct Answer: A
The vertex of the quadratic function given by f(x) = ax^2 + bx + c can be found using the formula (-b/(2a), f(-b/(2a))). Here, a = 1, b = -4, leading to x = 2 and f(2) = -1.
Q6
Medium
For the function f(x) = -2x^2 + 8x - 6, what is the maximum value?
A.
0
B.
4
C.
6
D.
8
Show Answer & Explanation
Correct Answer: B
The maximum value of a downward-opening quadratic function occurs at the vertex, found using x = -b/(2a). Here, f(4) = -2(4)^2 + 8(4) - 6 = 4.
Q7
Medium
Which of the following represents the graph of the function f(x) = |x - 2|?
A.
A V-shape with vertex at (2,0)
B.
A U-shape with vertex at (0,2)
C.
A horizontal line at y = 2
D.
A straight line with a slope of 1
Show Answer & Explanation
Correct Answer: A
The function f(x) = |x - 2| forms a V-shape because it represents the absolute value of a linear expression. The vertex is at (2, 0), where the function changes direction.
Q8
Hard
Let f(x) = 2x^2 - 4x + 1. What is the vertex of the parabola represented by this function?
A.
(1, -1)
B.
(2, -3)
C.
(0, 1)
D.
(4, 1)
Show Answer & Explanation
Correct Answer: A
The vertex can be found using the formula x = -b/(2a). Here, a = 2 and b = -4, so x = 4/4 = 1. Substituting x = 1 back into the function gives f(1) = 2(1)^2 - 4(1) + 1 = -1. Therefore, the vertex is (1, -1).
Q9
Hard
Consider the function f(x) = 2x^3 - 9x^2 + 12x - 4. What is the local maximum of the function?
A.
4
B.
2
C.
3
D.
5
Show Answer & Explanation
Correct Answer: C
To find the local maximum, we calculate the derivative f'(x) and set it to zero. The local maximum occurs at x=3, giving f(3)=3.
Q10
Hard
A quadratic function is defined by f(x) = ax^2 + bx + c. If the vertex of the parabola lies at the point (4, -5) and the parabola opens upwards, what can be inferred about 'a'?
A.
a > 0
B.
a < 0
C.
a = 0
D.
a = 1
Show Answer & Explanation
Correct Answer: A
Since the parabola opens upwards and the vertex is (4, -5), we know that 'a' must be positive for the function to have a minimum at the vertex.
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Hàm số và Đồ thị — THPT (Vietnam) THPT Toán Practice Questions Online
This page contains 150 practice MCQs for the chapter Hàm số và Đồ thị in THPT (Vietnam) THPT Toán. The questions are organized by difficulty — 45 easy, 77 medium, 28 hard — so you can choose the right level for your preparation.
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