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Answer 1

The piecewise equation for the function shown in the diagram is $f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.$

What is an equation?

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

From the diagram using the point (-6, 0.5) and (-1, 5):

y - 0.5 = [(5 - 0.5)/(-1 - (-6))](x - (-6))

y = (9/10)x + 5.9

Also, using the point (2, 1) and (4, -4):

y - 1 = [(-4 - 1)/(4 - 2)](x - 2)

y = -(5/2)x + 6

The piecewise equation for the function shown in the diagram is $f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.$

Find out more on equation at: brainly.com/question/2972832

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