# DETERMINE WHETHER EACH GIVEN IS AN EXPONENTIAL FUNCTION

An exponential function is non linear function of the form

y = abx, where a ≠ 0 and b ≠ 1 and b > 0

• Where a > 0 and b > 1, then the function is an exponential growth function.
• Where a > 0 and 0 < b < 1, then the function is an exponential decay function.

Determine which functions are exponential functions. For those that are not, explain why they are not exponential functions.

Problem 1 :

f(x) = 2x + 7

Solution :

f(x) = 2x + 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) = x2

Solution :

g(x) = x2

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) = 1x

Solution :

h(x) = 1x

Here, a = 1, b = 1

Since, the function is a constant function.

Problem 4 :

f(x) = xx

Solution :

f(x) = xx

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) = -3x + 1 + 5

Solution :

f(x) = -1(3x + 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 = abx. So, it i s not an exponential function.

Since it is in the form of y = ax + b, it is a linear function.

## Recent Articles

1. ### Finding Range of Values Inequality Problems

May 21, 24 08:51 PM

Finding Range of Values Inequality Problems

2. ### Solving Two Step Inequality Word Problems

May 21, 24 08:51 AM

Solving Two Step Inequality Word Problems