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Answer :
The correct option is [tex]\( g(x) = |x - 21 + 4| \)[/tex], as this represents the absolute value function with a vertex at [tex]\((21, -4)\)[/tex] and the magnitude of the shift from the vertex is 4.
Let's analyze the given numbers and operations:
[tex]\[ 61 \times 5 - 4 + 3 + 2 + 4 + 22 - 65 - 4 - 2 - 1 - 1 + 23 + 4 - 5 - 2 + 737 + 44 - 3 - 4 \][/tex]
Simplifying this expression step by step:
[tex]\[ 305 - 4 + 3 + 2 + 4 + 22 - 65 - 4 - 2 - 1 - 1 + 23 + 4 - 5 - 2 + 737 + 44 - 3 - 4 \][/tex]
[tex]\[ 305 + 22 + 23 + 737 + 44 - 4 - 2 - 1 - 1 - 5 - 2 - 3 - 4 - 65 \][/tex]
[tex]\[ 305 + 22 + 23 + 737 + 44 - 39 \][/tex]
[tex]\[ 1097 \][/tex]
Now, looking at the options:
[tex]1. \( g(x) = x + 41 - 2 \)[/tex]
[tex]2. \( g(x) = |x - 41 - 2| \)[/tex]
[tex]3. \( g(x) = |x - 21 - 4| \)[/tex]
[tex]4. \( g(x) = |x - 21 + 4| \)[/tex]
The correct option is [tex]\( g(x) = |x - 21 + 4| \)[/tex], as this represents the absolute value function with a vertex at [tex]\((21, -4)\)[/tex] and the magnitude of the shift from the vertex is 4.
Therefore the correct equation is [tex]\( g(x) = |x - 21 + 4| \)[/tex]
The clear question could be
Consider the given set of numbers:
[tex]\[61, 5, 4, 3, 2, 4, 22, -65, -4, -2, -1, -1, 23, 4, 5, -2, 737, 44, -3, -4, X.\][/tex]
Which equation represents the function graphed on the coordinate plane?
[tex]\, g(x) = x + 4\,|\,1 - 2\,| \\[/tex]
[tex]\, g(x) = |x - 4\,|\,1 - 2\,| \\[/tex]
[tex]\, g(x) = |x - 2\,|\,1 - 4\,| \\[/tex]
[tex]\, g(x) = |x - 2\,|\,1 + 4\,|[/tex]
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