What is the value of e^0?
A
0
B
1
C
e
D
Undefined
Analysis & Theory
Any number raised to the power 0 is 1, including e^0 = 1.
What is the derivative of e^x?
A
x·e^(x−1)
B
e^(x)
C
x·e^x
D
ln(x)
Analysis & Theory
The derivative of e^x is e^x.
The exponential function f(x) = a^x is defined for which values of a?
A
a > 0, a ≠ 1
B
a < 0
C
a = 1
D
a = 0
Analysis & Theory
Exponential functions are defined for a > 0 and a ≠ 1.
What is the inverse of the exponential function f(x) = e^x?
A
ln(x)
B
1/e^x
C
x^e
D
log(x)
Analysis & Theory
The inverse of e^x is ln(x).
What is the value of e^1?
A
0
B
1
C
e
D
Undefined
Analysis & Theory
By definition, e^1 = e ≈ 2.718.
Which of the following represents exponential growth?
A
y = e^x
B
y = e^(−x)
C
y = ln(x)
D
y = 1/x
Analysis & Theory
e^x grows rapidly as x increases, representing exponential growth.
What is the value of e^(ln x)?
A
x
B
ln(x)
C
e
D
1/x
Analysis & Theory
e and ln are inverse functions, so e^(ln x) = x.
Which function has the horizontal asymptote y = 0?
A
y = e^x
B
y = e^(−x)
C
y = ln(x)
D
Both A and B
Analysis & Theory
Both y = e^x and y = e^(−x) approach 0 as x → −∞ and ∞ respectively.
The graph of y = e^x
A
Passes through the origin
B
Passes through (0,1)
C
Is symmetric about x-axis
D
Is a straight line
Analysis & Theory
At x = 0, e^0 = 1, so the graph passes through (0,1).
If f(x) = e^(−x), then f(x) is:
A
Increasing
B
Decreasing
C
Constant
D
None of the above
Analysis & Theory
e^(−x) decreases as x increases, so the function is decreasing.