• 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]
