Question

A function can be represented by the equation g (z) =-(z) + 0.99. Complete the inequality to determine the range of this function.

Answer 1

To determine the range of the function \( g(z) = -z + 0.99 \), we start by analyzing the function itself.

1. **Identify the nature of the function**: The function is a linear equation with a slope of \(-1\), which means it is a decreasing function.

2. **Determine the behavior of \( g(z) \)**:
- As \( z \) increases (i.e., \( z \to \infty \)), \( g(z) \) will decrease towards \(-\infty\).
- As \( z \) decreases (i.e., \( z \to -\infty \)), \( g(z) \) will increase towards \( +\infty \).

Given this information, we can conclude:
- The maximum value of \( g(z) \) occurs as \( z \) approaches \(-\infty\), in which case \( g(z) \) approaches \( +\infty \).
- The minimum value of \( g(z) \) occurs as \( z \) approaches \( \infty \), in which case \( g(z) \) approaches \( -\infty \).

3. **Express the range**:
The range of \( g(z) \) can be expressed as all real numbers. Therefore, we can complete the inequality to represent the range of the function as:
\[
(-\infty, 0.99]
\]

So the complete inequality to determine the range of the function is:
\[
g(z) \leq 0.99
\]
Thus, the range of the function \( g(z) \) is \( (-\infty, 0.99] \).