f(x) = 2 for x ≤ 1, f(x) = ax + b for 1 < x < 3, and f(x) = 8 for x ≥ 3. For which a and b is f continuous everywhere?

Continuity & Differentiability · Question 51 of 125

Question 51

HardOriginal question

$f(x) = 2$ for $x \le 1$ , $f(x) = ax + b$ for $1 < x < 3$ , and $f(x) = 8$ for $x \ge 3$ . For which $a$ and $b$ is $f$ continuous everywhere?

a = 3,\ b = -1

Correct answerYour answer

a = -1,\ b = 3

Correct answerYour answer

a = 2,\ b = 0

Correct answerYour answer

a = 3,\ b = 5

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Worth noting

$a = 2,\ b = 0$ joins only at $x = 1$ ; the middle piece must meet both ends.

Ten questions from Continuity & Differentiability, at your own pace.

Ten questions from Continuity & Differentiability, at your own pace.