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Y = | x + 5 | + | x - 3 |

| x + 5 | = x + 5 x >= - 5

= - (x + 5) x <= - 5

| x + 3 | = x + 3 x >= -3

- (x+3) x <= -3

for x <= -5, y = - (x+5) - (x+3) = - 2 x - 8

for -5 <= x <= -3, y = ( x + 5 ) - ( x + 3 ) = 2

for x >= - 3, y = x + 5 + x + 3 = 2 x + 8

for x <= -5 , as x increases, y decreases. lowest value of y = 2 at x = -5

for -5 <= x <= -3, y = constant. = 2

for x > -3 , as x increases y increases.

there is a minumum value of y between - 5 <= x <= -3.

there is no upper bound at any value of x. y continuously increases or decreases otherwise.

| x + 5 | = x + 5 x >= - 5

= - (x + 5) x <= - 5

| x + 3 | = x + 3 x >= -3

- (x+3) x <= -3

for x <= -5, y = - (x+5) - (x+3) = - 2 x - 8

for -5 <= x <= -3, y = ( x + 5 ) - ( x + 3 ) = 2

for x >= - 3, y = x + 5 + x + 3 = 2 x + 8

for x <= -5 , as x increases, y decreases. lowest value of y = 2 at x = -5

for -5 <= x <= -3, y = constant. = 2

for x > -3 , as x increases y increases.

there is a minumum value of y between - 5 <= x <= -3.

*minimum value of y = 2*there is no upper bound at any value of x. y continuously increases or decreases otherwise.