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Compare the function f(x) = 4|x - 1| + 5 and the function g(x) modeled by the graph.What is the difference between the minimum values of f(x) and g(x)?Enter your answer in the box.

Compare The Function Fx 4x 1 5 And The Function Gx Modeled By The GraphWhat Is The Difference Between The Minimum Values Of Fx And GxEnter Your Answer In The Bo class=

Sagot :

• 1Given this function modeled by the graph:

[tex]g(x)[/tex]

You can identify that its vertex is:

[tex](-2,1)[/tex]

As you can see in the picture below:

Since the function opens upward, its vertex is the minimum point.

Therefore, you can identify that the minimum value of this function is the y-coordinate of the vertex:

[tex]y=1[/tex]

• Given the function:

[tex]f\mleft(x\mright)=4|x-1|+5[/tex]

You can identify that it is written in Vertex Form:

[tex]f\mleft(x\mright)=a|x-h|+k[/tex]

Where "h" is the x-coordinate of its vertex and "k" is the y-coordinate of the vertex. If:

[tex]a<0[/tex]

The function opens downward. And if:

[tex]a>0[/tex]

It opens upward.

In this case, you can identify that:

[tex]a=4[/tex]

Since it is greater than zero, you can determine that the function opens upward, and therefore, its minimum point is its vertex.

You can also identify that its vertex is:

[tex](1,5)[/tex]

Hence, its minimum value is:

[tex]y=5[/tex]

• In order to find the Difference between the minimum values of both functions, you have their minimum values:

[tex]5-1=4[/tex]

Hence, the answer is:

[tex]4[/tex]

View image LeighannA7396
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