Functions Practice Questions
IB (International Baccalaureate) · IB Math AA HL · 137 free MCQs with instant results and detailed explanations.
137
Total
43
Easy
70
Medium
24
Hard
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Sample Questions from Functions
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Q1
Easy
If f(x) = 2x + 3, what is f(5)?
A.
13
B.
10
C.
15
D.
8
Show Answer & Explanation
Correct Answer: A
To find f(5), substitute 5 into the function: f(5) = 2(5) + 3 = 10 + 3 = 13.
Q2
Easy
What is the domain of the function f(x) = 1/(x - 2)?
A.
x ∈ R, x ≠ 2
B.
x ∈ R
C.
x > 2
D.
x < 2
Show Answer & Explanation
Correct Answer: A
The function is undefined when the denominator is zero. Therefore, x cannot equal 2, making the domain x ∈ R, x ≠ 2.
Q3
Easy
If g(x) = x^2 - 4x + 4, what is the value of g(2)?
A.
0
B.
4
C.
8
D.
2
Show Answer & Explanation
Correct Answer: A
Substituting 2 into the function gives g(2) = (2)^2 - 4(2) + 4 = 4 - 8 + 4 = 0.
Q4
Medium
Consider the function f(x) = 2x^2 - 4x + 1. What is the vertex of this quadratic function?
A.
(1, -1)
B.
(2, -3)
C.
(1, -2)
D.
(0, 1)
Show Answer & Explanation
Correct Answer: A
The vertex form of a quadratic function is given by the formula (-b/2a, f(-b/2a)). Here, a = 2 and b = -4, so the x-coordinate of the vertex is 1. Plugging x = 1 back into the function yields f(1) = -1.
Q5
Medium
What is the range of the function f(x) = -2(x - 3)^2 + 5?
A.
y ≤ 5
B.
y ≥ 5
C.
y < 5
D.
y > 5
Show Answer & Explanation
Correct Answer: A
The function is in vertex form where the vertex is (3, 5). Since it opens downward (due to the negative coefficient), the maximum value is 5, meaning the range is all values less than or equal to 5.
Q6
Medium
The function f(x) = x^3 - 3x + 2 has what type of critical points?
A.
One local minimum and one local maximum
B.
Two local minimums
C.
No critical points
D.
One inflection point
Show Answer & Explanation
Correct Answer: A
To find critical points, we calculate the derivative, f'(x) = 3x^2 - 3. Setting f'(x) to zero gives critical points at x = 1 and x = -1, resulting in one local maximum and one local minimum.
Q7
Medium
If the function f(x) = e^(2x) - 4 has a root, what can be concluded about its behavior?
A.
It is decreasing everywhere.
B.
It is increasing everywhere.
C.
It has a local maximum.
D.
It has a horizontal asymptote.
Show Answer & Explanation
Correct Answer: B
The function f(x) = e^(2x) is always increasing because its derivative, f'(x) = 2e^(2x), is always positive. Therefore, it can only cross the x-axis once, confirming that it has a root.
Q8
Hard
The function g(x) = ln(x^2 + 1) - 2x has critical points where its derivative is zero. What value of x corresponds to a local maximum of g(x)?
A.
0
B.
1
C.
2
D.
None of the above
Show Answer & Explanation
Correct Answer: B
To find the critical points, compute the derivative g'(x) = (2x)/(x^2 + 1) - 2. Setting g'(x) = 0 leads to solving 2x = 2(x^2 + 1), resulting in the equation x^2 - x - 1 = 0. Solving this quadratic gives x = (1 ± √5)/2, but only x = 1 corresponds to a valid critical point that can be tested for local maximum via the second derivative test.
Q9
Hard
Consider the function f(x) = x^3 - 6x^2 + 9x. What is the local maximum value of this function?
A.
6
B.
9
C.
3
D.
0
Show Answer & Explanation
Correct Answer: B
To find the local maximum, we first find the derivative f'(x) = 3x^2 - 12x + 9. Setting f'(x) = 0 gives x = 1 and x = 3. Evaluating f(1) = 4 and f(3) = 9. Thus, the local maximum value is 9.
Q10
Hard
Let f(x) = x^3 - 6x^2 + 9x. What is the maximum value of f(x) on the interval [0, 5]?
A.
9
B.
8
C.
5
D.
12
Show Answer & Explanation
Correct Answer: A
To find the maximum value of f(x) on [0, 5], we first find the critical points by taking the derivative f'(x) = 3x^2 - 12x + 9 and setting it to zero. Solving gives x = 1 and x = 3. Evaluating f at these points and the endpoints, we find f(0) = 0, f(1) = 4, f(3) = 9, and f(5) = 10. The maximum value is at x = 3, where f(3) = 9.
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Functions — IB (International Baccalaureate) IB Math AA HL Practice Questions Online
This page contains 137 practice MCQs for the chapter Functions in IB (International Baccalaureate) IB Math AA HL. The questions are organized by difficulty — 43 easy, 70 medium, 24 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.