#1
Which of the following is a relation?
(2, 3)
ExplanationA relation is any set of ordered pairs, and (2, 3) represents an ordered pair.
#2
What is the range of the function f(x) = 2x - 1?
All real numbers
ExplanationThe function f(x) = 2x - 1 has a range of all real numbers.
#3
Which of the following is an example of a function?
y = x^2 + 1
ExplanationThe expression y = x^2 + 1 represents a function.
#4
If f(x) = x^2 and g(x) = 2x - 1, what is (f ∘ g)(x)?
4x^2 - 4x + 1
ExplanationThe composition (f ∘ g)(x) of the given functions is 4x^2 - 4x + 1.
#5
What is the domain of the function f(x) = √(x + 5)?
x ≥ -5
ExplanationThe domain of f(x) = √(x + 5) is x ≥ -5.
#6
If f(x) = 3x^2 + 5x - 2 and g(x) = 2x - 1, what is (f ∘ g)(x)?
6x^2 + 8x - 5
ExplanationThe composition (f ∘ g)(x) for the given functions is 6x^2 + 8x - 5.
#7
What is the domain of the function f(x) = 1/(x^2 - 4)?
x ≠ ±2
ExplanationThe domain of f(x) = 1/(x^2 - 4) is x ≠ ±2.
#8
What is the composition of functions f(x) = 2x + 1 and g(x) = x^2?
4x^2 + 4x + 1
ExplanationThe composition (f ∘ g)(x) for the given functions is 4x^2 + 4x + 1.
#9
Which of the following statements about relations is true?
Every function is a relation, but not every relation is a function.
ExplanationWhile every function is a relation, not every relation is a function.
#10
Which of the following is the graph of a one-to-one function?
A straight line passing the vertical line test
ExplanationA one-to-one function is represented by a graph where every vertical line intersects at most once.
#11
What is the period of the function f(x) = sin(x) + cos(x)?
2π
ExplanationThe period of the given function is 2π.
#12
What is the range of the function f(x) = e^x?
x ≥ 0
ExplanationThe range of f(x) = e^x is x ≥ 0.
#13
Which of the following is the graph of a many-to-one function?
A horizontal line
ExplanationA many-to-one function is represented by a graph where multiple inputs may map to the same output.
#14
What is the period of the function f(x) = tan(x)?
2π
ExplanationThe period of the tangent function is 2π.