Question

Which of the following statements is true about the function f(x)=5x+5

a.
The function is an increasing function.

b.
The function is a decreasing function.

c.
The function is a constant function.

d.
It is not a function

Answer 1

The given function is \( f(x) = 5x + 5 \).

To determine whether the function is increasing, decreasing, constant, or not a function, we can analyze its characteristics:

- **Increasing Function**: A function is increasing if its derivative is positive for all \( x \). The derivative of \( f(x) \) is \( f'(x) = 5 \), which is positive for all \( x \). Therefore, the function is increasing.

- **Decreasing Function**: Since the derivative is positive, the function is not decreasing.

- **Constant Function**: A constant function has a derivative of zero. Since \( f'(x) = 5 \), it is not a constant function.

- **Not a Function**: The expression \( f(x) = 5x + 5 \) clearly defines a function of \( x \).

Based on this analysis, the true statement is:

**a. The function is an increasing function.**