A constant function is a mathematical function that produces the same output value for every input value in its domain. For example, the function \( f(x) = 5 \) means that \( f(x) \) equals 5 regardless of the value of \( x \). Its graph is a straight horizontal line parallel to the x-axis, and it is often denoted as \( f(x) = c \), where \( c \) is a fixed constant. This type of function is continuous and has a constant rate of change of zero.
Table of Contents
- Part 1: Create An Amazing Constant Function Quiz Using AI Instantly in OnlineExamMaker
- Part 2: 20 Constant Function Quiz Questions & Answers
- Part 3: AI Question Generator – Automatically Create Questions for Your Next Assessment
Part 1: Create An Amazing Constant Function Quiz Using AI Instantly in OnlineExamMaker
Nowadays more and more people create Constant Function quizzes using AI technologies, OnlineExamMaker a powerful AI-based quiz making tool that can save you time and efforts. The software makes it simple to design and launch interactive quizzes, assessments, and surveys. With the Question Editor, you can create multiple-choice, open-ended, matching, sequencing and many other types of questions for your tests, exams and inventories. You are allowed to enhance quizzes with multimedia elements like images, audio, and video to make them more interactive and visually appealing.
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Part 2: 20 Constant Function Quiz Questions & Answers
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1. Question: What is a constant function?
A) A function where the output changes with the input.
B) A function where the output is always the same value regardless of the input.
C) A function that only uses constant numbers.
D) A function with a variable exponent.
Answer: B
Explanation: A constant function is defined as f(x) = c, where c is a constant, meaning the output remains the same for any input x.
2. Question: Which of the following is an example of a constant function?
A) f(x) = 2x + 3
B) f(x) = 5
C) f(x) = x^2
D) f(x) = 1/x
Answer: B
Explanation: f(x) = 5 is a constant function because it always returns the value 5, regardless of x.
3. Question: What is the graph of a constant function?
A) A straight line with a slope.
B) A parabola.
C) A horizontal line.
D) A vertical line.
Answer: C
Explanation: The graph of a constant function, like f(x) = c, is a horizontal line at y = c.
4. Question: For the function f(x) = 7, what is the range?
A) All real numbers
B) {7}
C) All positive numbers
D) All integers
Answer: B
Explanation: The range of a constant function f(x) = 7 is just the single value {7}, as it never varies.
5. Question: Is the function f(x) = -3 a constant function?
A) Yes
B) No
C) Only for positive x
D) Only for negative x
Answer: A
Explanation: f(x) = -3 is a constant function because it outputs -3 for every input x.
6. Question: What is the derivative of a constant function f(x) = k?
A) 1
B) x
C) 0
D) k
Answer: C
Explanation: The derivative of a constant function is zero, as there is no change in the output.
7. Question: Which equation represents a constant function?
A) y = x + 2
B) y = 4x
C) y = 10
D) y = x^3
Answer: C
Explanation: y = 10 is a constant function since y is always 10, irrespective of x.
8. Question: For f(x) = 0, what is the domain?
A) All real numbers except zero
B) Positive numbers only
C) All real numbers
D) Integers only
Answer: C
Explanation: The domain of a constant function like f(x) = 0 is all real numbers, as it is defined for every x.
9. Question: How many y-values does a constant function have?
A) Infinite
B) One
C) Two
D) None
Answer: B
Explanation: A constant function has only one y-value, as the output is the same for all inputs.
10. Question: Is f(x) = π a constant function?
A) Yes
B) No
C) Only for x > 0
D) Only for x = π
Answer: A
Explanation: f(x) = π is a constant function because π is a fixed constant value for any x.
11. Question: What is the slope of the graph of f(x) = 5?
A) 1
B) Undefined
C) 0
D) 5
Answer: C
Explanation: The graph is a horizontal line, so the slope is 0.
12. Question: Which function is not constant?
A) f(x) = 2
B) f(x) = 3x
C) f(x) = -1
D) f(x) = 0
Answer: B
Explanation: f(x) = 3x is not constant because the output changes with x.
13. Question: For a constant function, what happens to f(x) as x increases?
A) It increases
B) It decreases
C) It stays the same
D) It becomes undefined
Answer: C
Explanation: In a constant function, f(x) remains unchanged regardless of changes in x.
14. Question: What is the inverse of a constant function f(x) = 4?
A) f^{-1}(x) = 4
B) Not a one-to-one function, so no inverse
C) f^{-1}(x) = x/4
D) f^{-1}(x) = 1/x
Answer: B
Explanation: A constant function is not one-to-one, as multiple x values map to the same y, so it has no inverse.
15. Question: If f(x) = c, what is f(2) + f(3)?
A) 2c + 3c
B) c + c
C) 2 + 3
D) c
Answer: B
Explanation: For f(x) = c, f(2) = c and f(3) = c, so f(2) + f(3) = c + c = 2c, but the option matches as B implies 2c.
16. Question: Can a constant function be linear?
A) Yes
B) No
C) Only if the constant is zero
D) Only if the constant is positive
Answer: A
Explanation: A constant function is a special case of a linear function with a slope of zero.
17. Question: What is the y-intercept of f(x) = 6?
A) 0
B) 6
C) Undefined
D) 1
Answer: B
Explanation: For f(x) = 6, the graph is a horizontal line at y = 6, so the y-intercept is 6.
18. Question: In the function f(x) = k, what type of function is it if k is a fraction?
A) Not a function
B) Still a constant function
C) A quadratic function
D) An exponential function
Answer: B
Explanation: Regardless of the value of k, as long as it’s a fixed number, f(x) = k is a constant function.
19. Question: How does the range of f(x) = -2 compare to f(x) = 2?
A) The same
B) Different
C) One has no range
D) Only f(x) = 2 has a range
Answer: A
Explanation: Both are constant functions, so their ranges are single values: {-2} and {2}, but both are single-element sets.
20. Question: If g(x) = 1 and h(x) = 1, what is g(x) – h(x)?
A) 0
B) 1
C) x
D) Undefined
Answer: A
Explanation: g(x) – h(x) = 1 – 1 = 0, which is another constant function.
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Part 3: AI Question Generator – Automatically Create Questions for Your Next Assessment
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