An exponential function is non linear function of the form
y = ab^{x}, where a ≠ 0 and b ≠ 1 and b > 0
Determine which functions are exponential functions. For those that are not, explain why they are not exponential functions.
Problem 1 :
f(x) = 2^{x} + 7
Solution :
f(x) = 2^{x} + 7
Here, a = 1, b = 2
Since, the value of b is > 1. The given function f(x) is a exponential growth function.
Problem 2 :
g(x) = x^{2}
Solution :
g(x) = x^{2}
Here, a = 1, b = x
If it is a exponential function, the variable should be in the power. Since the power is 2, it must be a quadratic function.
Problem 3 :
h(x) = 1^{x}
Solution :
h(x) = 1^{x}
Here, a = 1, b = 1
Since, the function is a constant function.
Problem 4 :
f(x) = x^{x}
Solution :
f(x) = x^{x}
Here, a = 1, b = x
Since we have variable in the base and as well in power, it is not a exponential function. So, it is neither.
Problem 5 :
h(x) = 3 ⋅10^{-x}
Solution :
h(x) = 3 ⋅ 10^{-x}
h(x) = 3 ⋅ (1/10)^{x}
Here, a = 3, b = 1/10
Since, the value of b is 0 < b < 1. The given function h(x) is a exponential decay function.
Problem 6 :
f(x) = -3^{x + 1} + 5
Solution :
f(x) = -1(3^{x + 1} + 5)
a = 1, b = -3
Since, the value of b is 0 < b < 1. The given function f(x) is a exponential decay function.
Problem 7 :
g(x) = (-3)^{x + 1} + 5
Solution :
g(x) = (-3)^{x + 1} + 5
a = 1, b = -3
Since, the value of b is 0 < b < 1. The given function f(x) is a exponential decay function.
Problem 8 :
h(x) = 2x - 1
Solution :
h(x) = 2x - 1
Here, a = 1, b = 0
It is not in the form y = ab^{x}. So, it i s not an exponential function.
Since it is in the form of y = ax + b, it is a linear function.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM