Algebra Test Functions and Graphs 1 — Questions and Answers
Question 1: Which of the following relations is a function?
- {(1,2),(1,3),(2,4)}
- {(1,2),(2,3),(3,4)} (Correct answer)
- {(2,1),(2,3),(2,5)}
- {(0,0),(1,1),(1,-1)}
Correct answer: {(1,2),(2,3),(3,4)}
A function requires each input to have exactly one output; only the second set has no repeated x-values.
Question 2: What is the domain of f(x) = √(x - 3)?
- x ≥ 0
- x ≥ 3 (Correct answer)
- x > 3
- All real numbers
Correct answer: x ≥ 3
The radicand must be non-negative: x - 3 ≥ 0, so x ≥ 3.
Question 3: If f(x) = 3x - 2, what is f(4)?
- 6
- 8
- 10 (Correct answer)
- 12
Correct answer: 10
f(4) = 3(4) - 2 = 10.
Question 4: The vertical line test determines whether a graph is:
- A linear equation
- A function (Correct answer)
- A polynomial
- An inequality
Correct answer: A function
The vertical line test checks if any vertical line intersects the graph more than once; if not, it is a function.
Question 5: What is the range of f(x) = x² for all real x?
- All real numbers
- y ≥ 0 (Correct answer)
- y > 0
- y ≤ 0
Correct answer: y ≥ 0
Since x² ≥ 0 for all real x, the range is y ≥ 0.
Question 6: What notation means 'f composed with g'?
- f · g
- f + g
- f ∘ g (Correct answer)
- f ÷ g
Correct answer: f ∘ g
Function composition is written f ∘ g, meaning f(g(x)).
Algebra Test Functions and Graphs 1
Which of the following relations is a function?