State the range of the function: f(x) = 5ex + 1

A)
(0, ∞)
B)
(1, ∞)
C)
(-1, ∞)
D)
(-∞, ∞)

To determine the range of the function f(x) = 5ex + 1, we need to consider the properties of the exponential function and the constant term.

The exponential function is defined as ex, where e is Euler's number, a constant value approximately equal to 2.71828. The value of ex always produces a positive number greater than 0, regardless of the value of x.

In this case, we have f(x) = 5ex + 1. Multiplying the exponential function by 5 does not change its positive nature, and adding 1 to the result also does not change the fact that it remains positive.

Therefore, f(x) = 5ex + 1 will always produce a positive range. You can see from the function that as x approaches negative infinity, the term 5ex approaches zero, but it will never truly reach zero. As x approaches positive infinity, the term 5ex grows without bound.

Hence, the range of f(x) = 5ex + 1 is (-∞, ∞), which means all real numbers.

Therefore, the correct answer is D) (-∞, ∞).

To find the range of the function f(x) = 5ex + 1, we need to determine the set of all possible values that the function can produce.

The exponential function ex is always positive for any value of x, so 5ex will also always be positive.

Since the function f(x) = 5ex + 1 is always positive and adding 1 to a positive number still results in a positive number, the range of the function is (1, ∞).

Therefore, the correct answer is B) (1, ∞).