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< .
Answers
Answered by
GPT-4o mini
To determine the range of the function \( g(z) = -z + 0.99 \), we need to understand how the function behaves.
The function \( g(z) \) is a linear function with a negative slope (-1), which means it will decrease as \( z \) increases. As \( z \) approaches \( -\infty \), \( g(z) \) approaches \( +\infty \), and as \( z \) approaches \( +\infty \), \( g(z) \) approaches \( -\infty \).
Therefore, the range of the function will be all real numbers. In interval notation, the range can be written as:
\[
(-\infty, +\infty)
\]
In terms of the requested inequality format, this could be represented as:
\[
-\infty < g(z) < +\infty
\]
However, to match the format you provided, it can also be written as:
\[
-z + 0.99 < z < +\infty
\]
Thus, we fill in the blanks as follows:
\[
-\infty < g(z) < +\infty
\]
So the range of \( g(z) \) can be summarized with \( < z < \), indicating that \( z \) itself can take on any value.
The function \( g(z) \) is a linear function with a negative slope (-1), which means it will decrease as \( z \) increases. As \( z \) approaches \( -\infty \), \( g(z) \) approaches \( +\infty \), and as \( z \) approaches \( +\infty \), \( g(z) \) approaches \( -\infty \).
Therefore, the range of the function will be all real numbers. In interval notation, the range can be written as:
\[
(-\infty, +\infty)
\]
In terms of the requested inequality format, this could be represented as:
\[
-\infty < g(z) < +\infty
\]
However, to match the format you provided, it can also be written as:
\[
-z + 0.99 < z < +\infty
\]
Thus, we fill in the blanks as follows:
\[
-\infty < g(z) < +\infty
\]
So the range of \( g(z) \) can be summarized with \( < z < \), indicating that \( z \) itself can take on any value.