Asked by Maria
Find the constants a & b such that the function f(x)={2 if ≤ -1
{ax+b if -1<x<3
{-2 if x ≥3
is continuous on the entire real line
{ax+b if -1<x<3
{-2 if x ≥3
is continuous on the entire real line
Answers
Answered by
Reiny
the left-side transition point is (-1,2)
so (-1,2) should satisfy y = ax+b
2 = -a + b
the right-side transition point is (3, -2)
so (3,-2) should also satisfy y = ax + b
-2 = 3a + b
subtract those two equations
4a = -4
a = -1
then b = 2+a = 2-1 = 1
a=-1 , b=1
so (-1,2) should satisfy y = ax+b
2 = -a + b
the right-side transition point is (3, -2)
so (3,-2) should also satisfy y = ax + b
-2 = 3a + b
subtract those two equations
4a = -4
a = -1
then b = 2+a = 2-1 = 1
a=-1 , b=1
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.