Respuesta :
The vertex of the given modulus function is (3,-7).
Given information:
The given modulus function is,
[tex]f(x)=|x-3|-7[/tex]
It is required to find the vertex of the given function.
What is the vertex of a modulus function?
Modulus function is in the shape of V. The notch of V is the vertex of the function.
The given function can be defined as,
[tex]f(x)=x-10;x\geq3\\ f(x)=-x-4;x<3[/tex]
From the above function, it can be concluded that the vertex of the function should be (3,-7). Also shown in the attached image.
See the attached image.
Therefore, the vertex of the given modulus function is (3,-7).
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![Ver imagen aksnkj](https://us-static.z-dn.net/files/d14/05815f8bac7d64f534de4a4bbd0d62ce.png)
The vertex of the graph of f(x) is (-3, 7).
Given that
Graph; [tex]\rm f(x) = |x + 3| + 7[/tex]
We have to determine
What is the vertex of the graph of f(x)?
According to the question
The standard form of the absolute value function is;
[tex]\rm y = a|x-h|+k[/tex]
Where h and k are the vertexes of the function.
Graph; [tex]\rm f(x) = |x + 3| + 7[/tex]
Converting the equation into the standard form the absolute value function;
[tex]\rm f(X)=|x + 3| + 7\\ \\ f(x) = |x-(-3)|+7[/tex]
On comparing with the standard absolute value function the vertices of the graph f(x).
h = -3 and k = 7
Hence, the vertex of the graph of f(x) is (-3, 7).
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