We're glad you stopped by On a coordinate plane an absolute value graph has a vertex at tex 1 3 tex Which equation represents the function graphed on the coordinate. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
To determine which equation represents the function of an absolute value graph with a vertex at [tex]\((1, 3)\)[/tex], we start by understanding the general form of an absolute value function. The equation is generally written as:
[tex]\[ g(x) = |x - h| + k \][/tex]
Where [tex]\((h, k)\)[/tex] is the vertex of the graph.
For this problem, the vertex given is [tex]\((1, 3)\)[/tex]. So, we can substitute these values into the general equation:
- [tex]\(h = 1\)[/tex]
- [tex]\(k = 3\)[/tex]
This gives the equation:
[tex]\[ g(x) = |x - 1| + 3 \][/tex]
Now, we need to find the matching equation from the given options:
1. [tex]\(g(x)=|x+1|+3\)[/tex]
2. [tex]\(g(x)=|x+3|-1\)[/tex]
3. [tex]\(g(x)=|x-1|+3\)[/tex]
4. [tex]\(g(x)=|x+3|+1\)[/tex]
By comparing, the equation that matches our derived equation is:
[tex]\[ g(x)=|x-1|+3 \][/tex]
Therefore, the correct answer is:
[tex]\[ g(x)=|x-1|+3 \][/tex]
[tex]\[ g(x) = |x - h| + k \][/tex]
Where [tex]\((h, k)\)[/tex] is the vertex of the graph.
For this problem, the vertex given is [tex]\((1, 3)\)[/tex]. So, we can substitute these values into the general equation:
- [tex]\(h = 1\)[/tex]
- [tex]\(k = 3\)[/tex]
This gives the equation:
[tex]\[ g(x) = |x - 1| + 3 \][/tex]
Now, we need to find the matching equation from the given options:
1. [tex]\(g(x)=|x+1|+3\)[/tex]
2. [tex]\(g(x)=|x+3|-1\)[/tex]
3. [tex]\(g(x)=|x-1|+3\)[/tex]
4. [tex]\(g(x)=|x+3|+1\)[/tex]
By comparing, the equation that matches our derived equation is:
[tex]\[ g(x)=|x-1|+3 \][/tex]
Therefore, the correct answer is:
[tex]\[ g(x)=|x-1|+3 \][/tex]
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