Graph the Following Piecewise Functions:

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Exercise 1

f(x) = \left\{\begin{matrix} 2x + 4 \qquad if \qquad x > 0 \\ 4 - 2x \qquad if \qquad x < 0 \end{matrix}\right

Exercise 2

f(x) = \left\{\begin{matrix} 1 \qquad if \qquad x \leq 1\\ x \qquad if \qquad 1 < x \leq 3 \\ - x + 6 \qquad if \qquad 3 < x \leq 6 \\ 0 \qquad if \qquad 6 < x \end{matrix}\right

Exercise 3

f(x) = \left\{\begin{matrix} { x }^{ 2 } \qquad if \qquad x < 2 \\ 1 \qquad if \qquad x = 2 \\ 4 \qquad if \qquad x > 2 \end{matrix}\right

Exercise 4

f(x) = \left | x \right | - x

Exercise 5

f(x) = \frac { \left | x \right | }{ x }

Exercise 6

y = x + 1 - \left \lfloor x \right \rfloor

Exercise 7

y = 2x - \left \lfloor x \right \rfloor

Exercise 8

y = \left \lfloor \frac { x }{ 2 } \right \rfloor

Exercise 9

Find the analytical expression of the function.

 

 

Solution of exercise 1

Graph the piecewise function:

f(x) = \left\{\begin{matrix} 2x + 4 \qquad if \qquad x > 0 \\ 4 - 2x \qquad if \qquad x < 0 \end{matrix}\right

 

Solution of exercise 2

Graph the piecewise function:

f(x) = \left\{\begin{matrix} 1 \qquad if \qquad x \leq 1\\ x \qquad if \qquad 1 < x \leq 3 \\ - x + 6 \qquad if \qquad 3 < x \leq 6 \\ 0 \qquad if \qquad 6 < x \end{matrix}\right

 

Solution of exercise 3

Graph the piecewise function:

f(x) = \left\{\begin{matrix} { x }^{ 2 } \qquad if \qquad x < 2 \\ 1 \qquad if \qquad x = 2 \\ 4 \qquad if \qquad x > 2 \end{matrix}\right

Solution of exercise 4

Graph:

f(x) = \left | x \right | - x

x = 0

f(x) = \left\{\begin{matrix} -x - x \qquad if \qquad x < 0 \\ x - x \qquad if \qquad x \geq 0 \end{matrix}\right

f(x) = \left\{\begin{matrix} -2x \qquad if \qquad x < 0 \\ 0 \qquad if \qquad x \geq 0 \end{matrix}\right

Solution of exercise 5

Graph:

f(x) = \frac { \left | x \right | }{ x }

x = 0

f(x) = \left\{\begin{matrix} \frac { -x }{ x } \qquad if \qquad x < 0 \\ \frac { x }{ x } \qquad if \qquad x \geq 0 \end{matrix}\right

f(x) = \left\{\begin{matrix} -1 \qquad if \qquad x < 0 \\ 1 \qquad if \qquad x \geq 0 \end{matrix}\right

Solution of exercise 6

Graph:

y = x + 1 - \left \lfloor x \right \rfloor

x 0 0.5 0.9 1 1.5 1.9 2
y 1 1.5 1.9 1 1.5 1.9 1

Solution of exercise 7

Graph:

y = 2x - \left \lfloor x \right \rfloor

Solution of exercise 8

Graph the function:

y = \left \lfloor \frac { x }{ 2 } \right \rfloor

x 0 1 1.9 2 3 3.9 4
y 0 0 0 1 1 1 2

 

Solution of exercise 9

Find the analytical expression of the function.

f(x) = \left\{\begin{matrix} -x \qquad if \qquad x < 0\\ 1 \qquad if \qquad x = 0 \\ x \qquad if \qquad 0 < x < 2 \\ 1 \qquad if \qquad x \geq 3 \end{matrix}\right

 

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Hamza

Hi! I am Hamza and I am from Pakistan. My hobbies are reading, writing and playing chess. Currently, I am a student enrolled in the Chemical Engineering Bachelor program.