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What is the range of the function for the given domain?

[tex]\[
\begin{array}{l}
y = 2x - 5 \\
D: \{-2, 0, 2, 4\}
\end{array}
\][/tex]

Select the correct answer:
[tex]\[
\text{A. } R: \{-9, 0, -1, 3\} \\
\text{B. } R: \{9, -5, 9, 13\} \\
\text{C. } R: \{-9, -5, -1, 3\} \\
\text{D. } R: \{-9, 0, 9, 13\}
\][/tex]

Sagot :

GinnyAnswer
To find the range of the function [tex]\( y = 2x - 5 \)[/tex] for the given domain [tex]\( D = \{-2, 0, 2, 4\} \)[/tex], we need to substitute each value of the domain into the function and calculate the corresponding [tex]\( y \)[/tex] values.

Let's go through each value in the domain step-by-step:

1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ y = 2(-2) - 5 = -4 - 5 = -9 \][/tex]
So, when [tex]\( x = -2 \)[/tex], [tex]\( y = -9 \)[/tex].

2. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) - 5 = 0 - 5 = -5 \][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( y = -5 \)[/tex].

3. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 2(2) - 5 = 4 - 5 = -1 \][/tex]
So, when [tex]\( x = 2 \)[/tex], [tex]\( y = -1 \)[/tex].

4. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 2(4) - 5 = 8 - 5 = 3 \][/tex]
So, when [tex]\( x = 4 \)[/tex], [tex]\( y = 3 \)[/tex].

Now, we collect all the [tex]\( y \)[/tex] values obtained:
[tex]\[ R = \{-9, -5, -1, 3\} \][/tex]

Therefore, the range of the function for the given domain is [tex]\(\{-9, -5, -1, 3\}\)[/tex].

The correct answer is:
[tex]\[ R: \{-9, -5, -1, 3\} \][/tex]
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