Asked by kk
Is this the correct graph for the piecewise function f(x)=⎧⎩⎨⎪⎪12x+2 if x<−3−6 if −3≤x<3−x+4 if x≥3
? Why or why not?
(1 point)
No. The first function is graphed incorrectly.
No. The final function does not have the correct slope or interval.
No. The interval is incorrect for the final function, but everything else is correct.
Yes, they are all graphed correctly.
All Answers 1
Answered by
GPT-5 mini
AI
Answer: No. The interval is incorrect for the final function, but everything else is correct.
Reason: Evaluate the pieces at the boundaries:
- For x = −3 the middle piece applies (−3 ≤ x < 3), so f(−3) = −6 (closed dot at (−3, −6)); the left piece 1/2 x + 2 is valid only for x < −3, so it should end with an open dot at (−3, 0.5).
- For x = 3 the right piece applies (x ≥ 3), so f(3) = −3 + 4 = 1 (closed dot at (3, 1)); the middle constant −6 is only for x < 3 and should have an open dot at (3, −6).
If the graph instead shows the middle piece including x = 3 (closed dot at (3, −6)) or the right piece excluded at x = 3, then the interval for the final piece is wrong even if slopes and values elsewhere are correct.
Reason: Evaluate the pieces at the boundaries:
- For x = −3 the middle piece applies (−3 ≤ x < 3), so f(−3) = −6 (closed dot at (−3, −6)); the left piece 1/2 x + 2 is valid only for x < −3, so it should end with an open dot at (−3, 0.5).
- For x = 3 the right piece applies (x ≥ 3), so f(3) = −3 + 4 = 1 (closed dot at (3, 1)); the middle constant −6 is only for x < 3 and should have an open dot at (3, −6).
If the graph instead shows the middle piece including x = 3 (closed dot at (3, −6)) or the right piece excluded at x = 3, then the interval for the final piece is wrong even if slopes and values elsewhere are correct.
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