Question

Please help me solve this question.

------------- o -- -- (1 point) -6 Fill in the blanks to describe the given piecewise graph. Hint: In each row, the first blank should be the function, the second blank should be the lower bound for x, and the third blank should be the upper bound for x. !!! <x< 100 <x<

Answer 1

From the graph, we observe that

For -5 < x < 0

The graph passes through the points (-5, -1) and (0, -3)

Therefore, the slope m = (-3 - (-1)) / (0 - (- 5)) = - 2 / 5

Equation of the line is

y - (-1) = - (2 / 5) (x - (-5))

=> y + 1 = (-2/5)(x + 5)

=> y + 1 = (-2/5)x - 2

=> y = (-2/5)x - 3

Therefore, f(x) = (-2/5)x - 3

For 0 < x < 5

The graph passes through the points (5, -1) and (0, -3)

Therefore, the slope m = (-3 - (-1)) / (0 - (5)) = 2 / 5

Equation of the line is

y - (-1) = (2 / 5) (x - 5)

=> y + 1 = (2/5)(x - 5)

=> y + 1 = (2/5)x - 2

=> y = (2/5)x - 3

Therefore, f(x) = (2/5)x - 3

Therefore, the piecewise function is

f(x) =

-(2/5).x -3 (2/5).r -3 -5 < x < 0 0<x<5