Here is a compilation of 100 multiple-choice questions designed to test your knowledge of functions, domains, and ranges. Each question has four answer choices, with the correct answer provided.
Functions, Domain, and Range Quiz
- Which set of ordered pairs defines a function?
- A) {(1, 2), (2, 3), (1, 4)}
- B) {(1, 2), (2, 3), (3, 4)}
- C) {(1, 2), (2, 2), (2, 3)}
- D) {(1, 2), (1, 3), (1, 4)}
- Answer: B
- Determine the domain of the function f(x)=√x−4.
- A) x≥4
- B) x>4
- C) x≤4
- D) x<4
- Answer: A
- What is the range of the function f(x)=x2?
- A) All real numbers
- B) y≥0
- C) y>0
- D) y<0
- Answer: B
- Identify the domain of the function f(x)=x−31.
- A) x=3
- B) x>3
- C) All real numbers
- D) x<3
- Answer: A
- What is the range of the function g(x)=−x2+4?
- A) All real numbers
- B) y≤4
- C) y<4
- D) y≥4
- Answer: B
- Find the domain of h(x)=log(x−2).
- A) x>2
- B) x≥2
- C) All real numbers
- D) x<2
- Answer: A
- Which function is one-to-one?
- A) f(x)=x2
- B) f(x)=3x+1
- C) f(x)=sin(x)
- D) f(x)=∣x∣
- Answer: B
- Determine the domain of the function f(x)=x2−1x+1.
- A) All real numbers except x=1 and x=−1
- B) All real numbers
- C) x=1
- D) x≤1
- Answer: A
- What is the range of the function f(x)=ex?
- A) y≤0
- B) y<1
- C) y>0
- D) All real numbers
- Answer: C
- What is the domain of f(x)=x2+11?
- A) All real numbers
- B) x≥0
- C) x=1
- D) x<0
- Answer: A
- Which of the following is not a function?
- A) f(x)=3x+2
- B) f(x)=x2−x+1
- C) f(x)=√y (for y as a function of x)
- D) f(x)=∣x∣
- Answer: C
- What is the range of the function f(x)=2x?
- A) All real numbers
- B) y≥0
- C) y>0
- D) y<0
- Answer: C
- Determine the range of the function f(x)=cos(x).
- A) [−1,1]
- B) (0,1)
- C) All real numbers
- D) [0,1]
- Answer: A
- What is the minimum value of the function f(x)=∣x−2∣+3?
- A) 0
- B) 2
- C) 3
- D) 5
- Answer: C
- Find the domain of f(x)=√x1.
- A) All real numbers
- B) x>0
- C) x≥0
- D) x<0
- Answer: B
- Identify the range of the function f(x)=3x−2.
- A) All real numbers
- B) y>−2
- C) y≥−2
- D) y<0
- Answer: A
- For what values is the function f(x)=x3−5 defined?
- A) All real numbers
- B) x≥5
- C) x≤5
- D) x=0
- Answer: A
- Which function has a range of y<0?
- A) f(x)=−x2
- B) f(x)=x+1
- C) f(x)=x2+1
- D) f(x)=1/x where x>0
- Answer: A
- What is the domain of the function f(x)=sin−1(x)?
- A) [−1,1]
- B) (0,1)
- C) All real numbers
- D) [−π/2,π/2]
- Answer: A
- What is the range of f(x)=tan(x)?
- A) (−∞,∞)
- B) [−1,1]
- C) [0,∞)
- D) (−1,1)
- Answer: A
- Determine the domain of the function f(x)=√x+2.
- A) x≥−2
- B) x>−2
- C) All real numbers
- D) x≤−2
- Answer: A
- What is the domain of the function f(x)=x3+3x?
- A) All real numbers
- B) x≥0
- C) x≤0
- D) x>0
- Answer: A
- What is the range of the function f(x)=∣x∣?
- A) All real numbers
- B) y≥0
- C) y<0
- D) y>0
- Answer: B
- Which of the following is not a valid domain for a function?
- A) x≥−1
- B) x=2
- C) All real numbers
- D) x=0 only
- Answer: D
- Identify the domain for the function f(x)=log(3−x).
- A) x<3
- B) x≥3
- C) x>3
- D) All real numbers
- Answer: A
- What is the range of f(x)=4−x2?
- A) y≤4
- B) y<4
- C) y≥0
- D) All real numbers
- Answer: A
- What is the domain of the function f(x)=x−32x+1?
- A) x=3
- B) All real numbers
- C) x>3
- D) x<3
- Answer: A
- What is the range of the function f(x)=√1−x2?
- A) y≤1
- B) y≥0
- C) y is between 0 and 1
- D) All real numbers
- Answer: C
- For f(x)=x2−4x+5, where is the vertex located?
- A) (2,1)
- B) (−2,1)
- C) (2,5)
- D) (4,0)
- Answer: A
- What is the domain of f(x)=x2+x−61?
- A) x=3
- B) x=2 and x=−3
- C) All real numbers
- D) x>0
- Answer: B
- What is the range of the function f(x)=⌊x⌋ (greatest integer function)?
- A) All integers
- B) All real numbers
- C) Positive integers
- D) Zero
- Answer: A
- What is the range of f(x)=x2+2?
- A) y≥2
- B) All real numbers
- C) y>2
- D) y<2
- Answer: A
- What condition must be met for a function f(x) to be even?
- A) f(−x)=−f(x)
- B) f(−x)=f(x)
- C) f(x+h)=f(x)+h
- D) None of the above
- Answer: B
- What is the domain of the quadratic function f(x)=ax2+bx+c where a=0?
- A) All real numbers
- B) x≥0
- C) x≤0
- D) x>0
- Answer: A
- What is the range of the function f(x)=−2x+3?
- A) All real numbers
- B) y>3
- C) y≤3
- D) y<0
- Answer: A
- What is the domain of f(x)=√x2−1?
- A) ∣x∣≥1
- B) x>1
- C) x=1
- D) All real numbers
- Answer: A
- What is the range of f(x)=x21?
- A) y>0
- B) y≥0
- C) All real numbers
- D) y<0
- Answer: A
- What is the domain of the piecewise function defined as:
f(x)={x+23x−4if x<1if x≥1
- A) x<1 or x≥1
- B) x=1
- C) All real numbers
- D) x>1
- Answer: A
- What is the range of f(x)=−√x?
- A) y≤0
- B) y≥0
- C) y<0
- D) All real numbers
- Answer: A
- What is the range of the function f(x)=sin(x)+1?
- A) [0,2]
- B) [−1,1]
- C) All real numbers
- D) (0,2)
- Answer: A
- What is the domain of the function f(x)=2x−1?
- A) x≥0
- B) All real numbers
- C) x≤0
- D) x>1
- Answer: B
- What is the range of the function f(x)=√x2+1?
- A) All real numbers
- B) y≥1
- C) y>1
- D) ∣y∣≥1
- Answer: B
- What does the vertical line test determine?
- A) If a relation is a function
- B) The range of a function
- C) The domain of a function
- D) None of the above
- Answer: A
- What is the range of f(x)=x+5?
- A) All real numbers
- B) y≥5
- C) y<5
- D) y∈Z
- Answer: A
- For the function f(x)=x4−4x2, where does the maximum point occur?
- A) (0,0)
- B) (±2,±4)
- C) (−1,3)
- D) None of the above
- Answer: B
- What is the domain of f(x)=1/√x?
- A) x≥0
- B) x>0
- C) All real numbers
- D) x<0
- Answer: B
- What is the range of f(x)=x−x2+6x−7?
- A) (−∞,0)
- B) All real numbers
- C) y<0
- D) y>0
- Answer: B
- What is the domain of f(x)=tan−1(x)?
- A) All real numbers
- B) (−2π,2π)
- C) [−1,1]
- D) None of the above
- Answer: A
- What is the range of the quadratic function f(x)=−x2+3x+4?
- A) y≤ max value
- B) y≥4
- C) All real numbers
- D) (−∞, max value)
- Answer: A
- What is the domain of the function f(x)=x−1x2+1?
- A) All real numbers except x=1
- B) x<1
- C) x≥1
- D) x=0
- Answer: A
- What is the range of the function f(x)=−∣x∣+3?
- A) y≤3
- B) y>0
- C) All real numbers
- D) y<3
- Answer: A
- Where does the minimum value of f(x)=x2+2x+1 occur?
- A) (0,1)
- B) (−1,0)
- C) (−1,0)
- D) None of the above
- Answer: B
- What is the domain of f(x)=√x−23x+1?
- A) x<2
- B) x≥2
- C) x>2
- D) All real numbers
- Answer: C
- What is the range of f(x)=2sin(x)?
- A) [−2,2]
- B) (0,2)
- C) All real numbers
- D) [0,2]
- Answer: A
- What is the domain of the function f(x)=x2−4x3?
- A) All real numbers
- B) x=2 and x=−2
- C) x>2
- D) None of the above
- Answer: B
- What is the range of f(x)=log(x−3)?
- A) All real numbers
- B) y>0
- C) y≤0
- D) y<3
- Answer: A
- For the function f(x)=2x+11, what is the domain?
- A) x=−21
- B) All real numbers
- C) x>0
- D) x≥0
- Answer: A
- What is the range of f(x)=x3−8?
- A) All real numbers
- B) y<0
- C) y≥−8
- D) y<−8
- Answer: A
- When does the minimum value of the function f(x)=x2+2x+1 occur?
- A) x=−1
- B) x=1
- C) x=0
- D) None of the above
- Answer: A
- What is the domain of f(x)=sin(x)1?
- A) All real numbers
- B) x=nπ where n∈Z
- C) x=2π+nπ
- D) None of the above
- Answer: B
- Where does the maximum value of the function f(x)=−x2+6x occur?
- A) (3,9)
- B) (0,0)
- C) (6,0)
- D) None of the above
- Answer: A
- What is the range of g(x)=√x−2?
- A) y≥−2
- B) All real numbers
- C) y>−2
- D) None of the above
- Answer: A
- What is the domain of f(x)=x2+1x2−1?
- A) All real numbers
- B) x=0
- C) x=±1
- D) None of the above
- Answer: A
- What is the range of f(x)=x1?
- A) All real numbers except 0
- B) All real numbers
- C) y<0
- D) y≥0
- Answer: A
- Does the function f(x)=7−3x have a maximum or minimum value?
- A) Maximum
- B) Minimum
- C) Neither max nor min
- D) Both max and min
- Answer: C
- Where does the minimum value of f(x)=x2+4 occur?
- A) x=0
- B) x=2
- C) x=−2
- D) None of the above
- Answer: A
- What is the range of f(x)=∣3−x∣?
- A) y≥0
- B) (−∞,3]
- C) All real numbers
- D) None of the above
- Answer: A
- What is the domain of f(x)=√2x+3?
- A) x≥−23
- B) x<−23
- C) All real numbers
- D) x>−3
- Answer: A
- What is the range of f(x)=−3x+1?
- A) All real numbers
- B) y≥1
- C) y<1
- D) y>1
- Answer: A
- For the function f(x)=e−x, what is the domain?
- A) All real numbers
- B) x>0
- C) x∈(0,1)
- D) x=1
- Answer: A
- For what values is the function g(x)=tan(x) defined?
- A) x=nπ+2π (where n∈Z)
- B) All real numbers
- C) x∈[0,π)
- D) None of the above
- Answer: A
- What is the range of h(x)=1−∣x∣?
- A) h≤1
- B) All real numbers
- C) h∈Z
- D) None of the above
- Answer: A
- When does the maximum value of f(x)=−2x2+8x−5 occur?
- A) x=48
- B) x=4
- C) x<0
- D) None of the above
- Answer: A
- What is the domain of f(x)=log(4−x2)?
- A) −2<x<2
- B) x>4
- C) All real numbers
- D) x<0
- Answer: A
- What is the range of f(x)=x1+3?
- A) All real numbers
- B) y>3
- C) y≤3
- D) y=3
- Answer: D
- The function f(x)=x2−2x+3 can be rewritten as:
- A) (x−1)2+2
- B) (x−2)2+1
- C) (x+2)2−1
- D) None of the above
- Answer: A
- What is the minimum value of f(x)=(x−3)2+1?
- A) 1
- B) 2
- C) 3
- D) 0
- Answer: A
- How is the domain of a function defined?
- A) Set of possible output values
- B) Set of possible input values
- C) Graph of the function
- D) None of the above
- Answer: B
- What is the domain of the function f(x)=x2+11?
- A) All real numbers
- B) x>0
- C) x<0
- D) None of the above
- Answer: A
- What is the range of g(x)=−x2−4?
- A) All real numbers
- B) y<−4
- C) y≤−4
- D) y≥−4
- Answer: C
- What is the domain of the function f(x)=sec(x)?
- A) All real numbers
- B) x=nπ+2π
- C) x∈[0,π)
- D) All integers
- Answer: B
- What is the domain of the function f(x)=x2−9x−5?
- A) x=3 and x=−3
- B) All real numbers
- C) x<3
- D) None of the above
- Answer: A
- How is the maximum of the function g(x)=−3x2+12x−5 found?
- A) According to x=−2ab
- B) At the vertex
- C) Both answers are valid
- D) None of the above
- Answer: C
- What is the range of f(x)=1+x2?
- A) y>1
- B) All real numbers
- C) y≤1
- D) y≥0
- Answer: A
- What type of function is h(x)=2x+1?
- A) A linear function
- B) A quadratic function
- C) A cubic function
- D) None of the above
- Answer: A
- Where does the maximum value of the function defined by f(x)=−x2−6x−8 occur?
- A) (−3,1)
- B) (−6,0)
- C) None of the above
- D) Minimum value
- Answer: A
- What is the domain of the function g(x)=sin−1(x)+cos−1(x)?
- A) −1≤x≤1
- B) All real numbers
- C) x=0
- D) None of the above
- Answer: A
- What is the range of a function f(x) from [a,b] generally?
- A) All values between a and b
- B) y>b
- C) All values below a
- D) None of the above
- Answer: A
- For the function defined as f(x)=x+1x2−1, what is its domain?
- A) All real numbers except x=−1
- B) x≥−1
- C) x>0
- D) None of the above
- Answer: A
- What is the range of f(x)=3cos(x)+2?
- A) [2,5]
- B) (−5,5)
- C) All real numbers
- D) None of the above
- Answer: A
- What is the domain of f(x)=x√x−4?
- A) x≥4
- B) x<4
- C) All real numbers
- D) None of the above
- Answer: A
- If f(x)=2−x4, what is the domain?
- A) All real numbers except x=2
- B) x<2
- C) x>2
- D) None of the above
- Answer: A
- What is the range of f(x)=log(x+1)?
- A) All real numbers
- B) (−∞,0)
- C) [0,∞)
- D) None of the above
- Answer: A
- Where does the maximum of f(x)=−x2+2x occur?
- A) Vertex (1,1)
- B) (2,0)
- C) None of the above
- x=−−2
- D) Vertex (0,0)
- Answer: A
- What is the domain of g(x)=ex2?
- A) All real numbers
- B) x=0
- C) x≥0
- D) None of the above
- Answer: A
- What is the range of f(x)=x2−5?
- A) y≥−5
- B) y>−5
- C) All real numbers
- D) y<0
- Answer: A
- What is the domain of the function f(x)=√4−x2?
- A) −2≤x≤2
- B) All real numbers
- C) x<4
- D) None of the above
- Answer: A
- What is the range of f(x)=x3+1?
- A) All real numbers except 1
- B) y>
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