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A function is defined by f(x) = 1 for x ≤ 2, f(x) = ax + b for 2 < x < 4, and f(x) = 7 for x ≥ 4…

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A function is defined by $f(x) = 1$ for $x \le 2$ , $f(x) = ax + b$ for $2 < x < 4$ , and $f(x) = 7$ for $x \ge 4$ . Find $a$ and $b$ so that $f$ is continuous everywhere.

Need a reminder? The key ideaShow

On an interval, check every joining point of a piecewise function: the left-hand limit, the right-hand limit and the value must be equal. Sums, products, quotients (with a nonzero denominator) and compositions of continuous functions are continuous.

The worked solution

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A function is defined by f(x) = 1 for x ≤ 2, f(x) = ax + b for 2 < x < 4, and f(x) = 7 for x ≥ 4…

The worked solution

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