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Exercises for Question Type 8: Determining continuity of piecewise models - IB | RevisionDojo

Question 1

Skill question

Determine $b$ so that

f(x)=\begin{cases} 3x+b,&x<2,\\ 5x+1,&x\ge2 \end{cases}

is continuous at $x=2$ .

Question 2

Skill question

Determine $k$ such that

f(x)=\begin{cases} kx+3,&x<3,\\ 2x-1,&x\ge3 \end{cases}

is continuous at $x=3$ .

Question 3

Skill question

Determine $m$ so that

f(x)=\begin{cases} (x-1)^2,&x<1,\\ m x+1,&x\ge1 \end{cases}

is continuous at $x=1$ .

Question 4

Skill question

Find the value of $a$ such that the function

f(x)=\begin{cases} x+2,&x<1,\\ a x-3,&x\ge1 \end{cases}

is continuous at $x=1$ .

Question 5

Skill question

Find $a$ so that the function

f(x)=\begin{cases} \displaystyle\frac{x^2-1}{x-1},&x\neq1,\\ a,&x=1 \end{cases}

is continuous at $x=1$ .

Question 6

Skill question

Find $k$ so that

f(x)=\begin{cases} \dfrac{\sin x}{x},&x\neq0,\\ k,&x=0 \end{cases}

is continuous at $x=0$ .

Question 7

Skill question

Find $a$ so that

f(x)=\begin{cases} x^2+a x+1,&x\le1,\\ 2a x+1,&x>1 \end{cases}

is continuous at $x=1$ .

Question 8

Skill question

Find $a$ so that

f(x)=\begin{cases} x^3-8,&x<2,\\ a(x-2),&x\ge2 \end{cases}

is continuous at $x=2$ .

Question 9

Skill question

Express $b$ in terms of $a$ so that the function

f(x)=\begin{cases} x^2,&x\le2,\\ a x+b,&x>2 \end{cases}

is continuous at $x=2$ .

Question 10

Skill question

Determine $a$ so that

f(x)=\begin{cases} \sqrt{x+3},&-3\le x<1,\\ a x^2+1,&x\ge1 \end{cases}

is continuous at $x=1$ .

Question 11

Skill question

Determine $a$ so that

f(x)=\begin{cases} x+2,&x<0,\\ a x^2+2,&0\le x<1,\\ 2x+1,&x\ge1 \end{cases}

is continuous on its domain.

Question 12

Skill question

Given the piecewise function

f(x)=\begin{cases} a x+b,&x<1,\\ 2x+1,&1\le x<3,\\ c x-1,&x\ge3, \end{cases}

find $b$ and $c$ in terms of $a$ so that $f$ is continuous at both $x=1$ and $x=3$ .

Question Type 8: Determining continuity of piecewise models Exercises