Question

A function can be represented by the equation g(z)=−z+0.99
. Complete the inequality to determine the range of this function.(1 point)
The range is represented by the inequality
<z<
.

Answer 1

To find the range of the function \( g(z) = -z + 0.99 \), we first look at the behavior of the function.

Since it is a linear function with a negative slope, it will decrease as \( z \) increases. The maximum value of \( g(z) \) occurs when \( z \) is at its minimum value, and the minimum value of \( g(z) \) occurs when \( z \) is at its maximum value.

Assuming \( z \) can take any real number, we can analyze this function:

1. As \( z \) approaches positive infinity, \( g(z) = -z + 0.99 \) approaches negative infinity.
2. As \( z \) approaches negative infinity, \( g(z) = -z + 0.99 \) approaches positive infinity.

Thus, the function can take on all real values.

Therefore, we can express the range of \( g(z) \) as:

\[
-\infty < g(z) < \infty
\]

If we were asked to fill in the specific values in your inequality format, it would be:

\[
-\infty < g(z) < \infty
\]

So the completed inequality would be:

\[
< z <
\]

for the real numbers, indicating that \( g(z) \) can take any value from \(-\infty\) to \(+\infty\).