Functions Practice Questions
IB (International Baccalaureate) · IB Math AI SL · 147 free MCQs with instant results and detailed explanations.
147
Total
37
Easy
80
Medium
30
Hard
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Sample Questions from Functions
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Q1
Easy
If f(x) = 2x + 3, what is f(4)?
A.
11
B.
12
C.
8
D.
10
Show Answer & Explanation
Correct Answer: A
To find f(4), substitute x with 4 in the function: f(4) = 2(4) + 3 = 8 + 3 = 11.
Q2
Easy
What is the range of the function f(x) = 2x + 3?
A.
All real numbers
B.
All positive numbers
C.
All integers
D.
All negative numbers
Show Answer & Explanation
Correct Answer: A
The function f(x) = 2x + 3 is a linear function, which means it can take any real number as input. As x approaches positive or negative infinity, f(x) will also approach positive or negative infinity respectively. Thus, the range is all real numbers.
Q3
Easy
Which of the following functions represents a vertical shift of 3 units upwards from the function g(x) = x^3?
A.
f(x) = x^3 + 3
B.
f(x) = x^3 - 3
C.
f(x) = x^3 * 3
D.
f(x) = 3x^3
Show Answer & Explanation
Correct Answer: A
Vertical shifts are achieved by adding or subtracting a constant from a function. In this case, to shift g(x) = x^3 upwards by 3 units, we add 3 to the function, resulting in f(x) = x^3 + 3.
Q4
Medium
Which of the following functions is a one-to-one function?
A.
f(x) = x^2
B.
f(x) = e^x
C.
f(x) = sin(x)
D.
f(x) = |x|
Show Answer & Explanation
Correct Answer: B
A function is one-to-one if it passes the horizontal line test, meaning no horizontal line intersects the graph more than once. The function f(x) = e^x is strictly increasing, hence it is one-to-one. In contrast, x^2 and |x| are not one-to-one as they have multiple x values yielding the same y value, while sin(x) is periodic.
Q5
Medium
If f(x) = 4x - 7, what is f(3) and what does it represent in terms of function outputs?
A.
5, the output at x = 3
B.
-5, the output at x = 3
C.
0, the output at x = 4
D.
1, the output at x = 2
Show Answer & Explanation
Correct Answer: A
To find f(3), substitute x with 3 in the function: f(3) = 4(3) - 7 = 12 - 7 = 5. This value represents the output of the function when the input is 3.
Q6
Medium
Which of the following functions represents a quadratic function?
A.
f(x) = 2x + 3
B.
f(x) = x^2 - 4x + 4
C.
f(x) = 1/x
D.
f(x) = 3√x
Show Answer & Explanation
Correct Answer: B
A quadratic function is characterized by the highest degree of 2. The function f(x) = x^2 - 4x + 4 has x raised to the power of 2, thus it is a quadratic function.
Q7
Medium
For which value of k does the function f(x) = -x^2 + kx have a maximum value?
A.
k = 0
B.
k = 2
C.
k = 1
D.
k = 3
Show Answer & Explanation
Correct Answer: B
The function is a downward-opening parabola since the coefficient of x^2 is negative. The maximum value occurs at k = 2, which determines the vertex's x-coordinate in the standard form.
Q8
Hard
Consider the function f(x) = x^3 - 6x^2 + 9x. What is the minimum value of f(x) on the interval [0, 6]?
A.
0
B.
3
C.
6
D.
9
Show Answer & Explanation
Correct Answer: B
To find the minimum value, we first take the derivative f'(x) = 3x^2 - 12x + 9. Setting it to zero gives critical points at x = 1 and x = 3. Evaluating f(0) = 0, f(1) = 3, f(3) = 6, and f(6) = 9. The minimum occurs at x = 1, hence f(1) = 3.
Q9
Hard
Consider the function f(x) = x^2 - 4x + 7. What is the minimum value of f(x)?
A.
3
B.
4
C.
5
D.
6
Show Answer & Explanation
Correct Answer: A
The function f(x) = x^2 - 4x + 7 is a quadratic function which opens upwards. The minimum value occurs at the vertex, which can be found using the formula x = -b/(2a). Here, a = 1 and b = -4, so the x-coordinate of the vertex is x = 4/2 = 2. Plugging x = 2 back into the function gives f(2) = 2^2 - 4*2 + 7 = 4 - 8 + 7 = 3.
Q10
Hard
If the function g(x) = x^2 + kx + 4 has a minimum value of 1, what is the value of k?
A.
-2
B.
-4
C.
2
D.
4
Show Answer & Explanation
Correct Answer: A
The minimum value of a quadratic function ax^2 + bx + c occurs at x = -b/(2a). Here, k = -2 * 1 + 4 = 1, thus giving k = -2.
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Functions — IB (International Baccalaureate) IB Math AI SL Practice Questions Online
This page contains 147 practice MCQs for the chapter Functions in IB (International Baccalaureate) IB Math AI SL. The questions are organized by difficulty — 37 easy, 80 medium, 30 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.