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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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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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