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Making a piecewise function continuous practice problems

Choose the constant that makes a piecewise function continuous. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k x^{2} + 5 & x < -2 \\ 2 x + 3 & x \ge -2 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.199medium✓ Nihil obstat

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k x - 5 & x < 1 \\ 2 x - 1 & x \ge 1 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.200medium✓ Every equation proved

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k x^{2} - 4 & x < 2 \\ - x^{2} - 3 x - 2 & x \ge 2 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.201medium✓ Nihil obstat

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k + 3 x^{2} & x < 2 \\ 4 x + 4 & x \ge 2 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.202medium✓ Every equation proved

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k x + 5 & x < 1 \\ 2 - 2 x & x \ge 1 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.203medium✓ Every equation proved

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k - 3 x^{2} & x < 2 \\ 3 x + 2 & x \ge 2 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.204medium✓ Every equation proved

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k + 2 x^{2} & x < 0 \\ 2 x + 2 & x \ge 0 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.205medium✓ Every equation proved

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k + 3 x^{2} & x < 1 \\ - x^{2} - 3 x & x \ge 1 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.206medium✓ Every equation proved

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k - 2 x^{2} & x < 2 \\ x + 4 & x \ge 2 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.207medium✓ Every equation proved

Find the value of \( \displaystyle k \) that makes \( \displaystyle f(x) = \begin{cases} k x + 2 & x < 3 \\ 2 x & x \ge 3 \end{cases} \) continuous for all \( \displaystyle x \).

Problem 1.208medium✓ Every equation proved