Which of the following is a function?
A
Each input has two outputs
B
Every output has two inputs
C
Each input has exactly one output
D
Inputs and outputs are equal
Analysis & Theory
A function assigns exactly one output to each input.
The domain of a function is
A
The set of all possible outputs
B
The set of all inputs for which the function is defined
C
The set of all real numbers
D
The set of positive integers
Analysis & Theory
The domain is the set of all inputs where the function is defined.
Which of the following is NOT a function?
A
f(x) = x²
B
f(x) = √x
C
f(x) = 1/x
D
f(x) = ±√x
Analysis & Theory
f(x) = ±√x gives two outputs for one input, hence not a function.
What is the limit of f(x) = x² as x approaches 2?
A
2
B
4
C
6
D
8
Analysis & Theory
lim(x→2) x² = 4.
lim(x→0) (sin x)/x equals
A
0
B
1
C
Undefined
D
Infinity
Analysis & Theory
This is a standard limit: lim(x→0) (sin x)/x = 1.
If lim(x→a) f(x) exists, then
A
f(a) must be defined
B
f(a) must not be defined
C
Limit from left and right must be equal
D
f(x) is always continuous at x = a
Analysis & Theory
Limit exists only if left-hand and right-hand limits are equal.
Which of the following functions is continuous at x = 1?
A
f(x) = 1/x
B
f(x) = |x - 1|
C
f(x) = 1 if x ≠ 1, 0 if x = 1
D
f(x) = 1/(x - 1)
Analysis & Theory
|x - 1| is continuous everywhere including x = 1.
The limit of a constant function f(x) = 5 as x approaches any number is
A
0
B
5
C
Depends on x
D
Undefined
Analysis & Theory
The limit of a constant function is the constant itself.
Which function has a limit at x = 0?
A
f(x) = 1/x
B
f(x) = sin(1/x)
C
f(x) = x sin(1/x)
D
f(x) = 1/|x|
Analysis & Theory
x·sin(1/x) has limit 0 as x → 0, by the squeeze theorem.
If f(x) is continuous at x = a, then
A
lim(x→a) f(x) = f(a)
B
lim(x→a) f(x) does not exist
C
f(a) is undefined
D
f(x) has a jump at x = a
Analysis & Theory
Continuity at a point means limit exists and equals the function value.