Question

Find the range of the following peicewise functiom

Answer 1

answer is [0,11)

f(x) = x+4 is the first function

We plug in -4 for x in f(x) = x+4

f(-4) = -4 + 4 = 0

So the graph starts at (-4,0)

Now plug in 3 for x in f(x) = x+4

f(3) = 3 + 4 = 7

So the first function ends at (3,7)

Second function is f(x) = 2x - 1

We plug in 3 for x in f(x) = 2x-1

f(3) =2(3)-1 = 5

So the second graph starts at (3,5)

We plug in 6 for x in f(x) = 2x-1

f(6) =2(6)-1 = 11

So the second graph ends at (6,11)

3<=x<6 so 6 is excluded from x

The range of the following piece wise function is 0 to 11

answer is [0,11)

Answer 2

f(x) = x + 4 ; -4 ≤ x < 3

f(-4) = (-4) + 4

= 0

f(3) = (3) + 4

= 7

R: 0 ≤ y < 7 ⇒ [0, 7)

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f(x) = 2x - 1 ; 3 ≤ x < 6

f(3) = 2(3) - 1

= 6 - 1

= 5

f(6) = 2(6) - 1

= 12 - 1

= 11

R: 5 ≤ y < 11 ⇒ [5, 11)

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Now, put them together: [0, 7) U [5, 11) = [0, 11)

Answer: B