The function that models the graph is given as:[tex]f(x)=\left \{ {{-\frac{1}{3}x+\frac{4}{3} \ \ -8 < x < 2} \atop {-x^2+6\ \ -2 < x < 0}} \atop {6\ \ 0 < x < 4}, \ \ x+2\ \ 4 < x < 7 \right.[/tex]
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
The equation shown in the graph represents a piecewise function. Hence:
From the line through the point (-8, 4) and (-2, 2), the equation is f(x) = -(1/3)x + 4/3
From the curve through the point (-2, 2) and (0, 6), the equation is f(x) = -x² + 6
From the line through the point (0, 6) and (4, 6), the equation is f(x) = -6
From the line through the point (4, 6) and (7, 9), the equation is f(x) = x + 2
The function that models the graph is given as:[tex]f(x)=\left \{ {{-\frac{1}{3}x+\frac{4}{3} \ \ -8 < x < 2} \atop {-x^2+6\ \ -2 < x < 0}} \atop {6\ \ 0 < x < 4}, \ \ x+2\ \ 4 < x < 7 \right.[/tex]
Find out more on equation at: https://brainly.com/question/2972832
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