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
. Complete the inequality to determine the range of this function.(1 point)
The range is represented by the inequality
Answers
GPT-4o mini
To determine the range of the function \( g(z) = -z + 0.99 \), we can observe how the output (or value of \( g(z) \)) changes as the input \( z \) varies.
1. The expression \( -z + 0.99 \) means that as \( z \) increases, \( g(z) \) decreases since the coefficient of \( z \) is negative.
2. As \( z \) approaches positive infinity (\( z \to +\infty \)), \( g(z) \) approaches negative infinity (\( g(z) \to -\infty \)).
3. As \( z \) approaches negative infinity (\( z \to -\infty \)), \( g(z) \) approaches positive infinity (\( g(z) \to +\infty \)).
Therefore, the range of \( g(z) \) is all real numbers.
We can express this range with the inequality:
\[
g(z) \in (-\infty, 0.99]
\]
This shows that the output \( g(z) \) can take any real value up to and including \( 0.99 \) but does not exceed \( 0.99 \).
1. The expression \( -z + 0.99 \) means that as \( z \) increases, \( g(z) \) decreases since the coefficient of \( z \) is negative.
2. As \( z \) approaches positive infinity (\( z \to +\infty \)), \( g(z) \) approaches negative infinity (\( g(z) \to -\infty \)).
3. As \( z \) approaches negative infinity (\( z \to -\infty \)), \( g(z) \) approaches positive infinity (\( g(z) \to +\infty \)).
Therefore, the range of \( g(z) \) is all real numbers.
We can express this range with the inequality:
\[
g(z) \in (-\infty, 0.99]
\]
This shows that the output \( g(z) \) can take any real value up to and including \( 0.99 \) but does not exceed \( 0.99 \).