Answer:
The piecewise model of the function is
[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]
[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]
Step-by-step explanation:
we know that
The general form of absolute value equation is
[tex]f\left(x\right)=a\left|x-h\right|+k[/tex]
where
The variable a, tells us how far the graph stretches vertically, and whether the graph opens up or down
(h,k) is the vertex of the absolute value
In this problem we have
[tex]f\left(x\right)=0.7\left|x-4\right|+2[/tex]
we have
[tex]a=0.7[/tex]
The coefficient a is positive ----> the graphs open up
The vertex is the point (4,2)
Find the piecewise model
case 1) positive value
[tex]f(x)=0.7[(x-4)]+2[/tex]
[tex]f(x)=0.7x-2.8+2\\f(x)=0.7x-0.8[/tex]
Is a linear equation with positive slope
[tex](x-4)\geq 0\\x\geq 4[/tex]
The domain is the interval [4,∞)
case 2) negative value
[tex]f(x)=0.7[-(x-4)]+2[/tex]
[tex]f(x)=-0.7x+2.8+2\\f(x)=-0.7x+4.8[/tex]
Is a linear equation with negative slope
[tex](x-4)< 0\\x<4[/tex]
The domain is the interval (-∞,4)
[tex]x<4[/tex]
therefore
The piecewise model of the function is
[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]
[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]
