given-that-g-x-x-2-if-0-x-lt-2-x-2-if-2-x-lt-4-is-periodic-of-period-4-sketch-the-curve-for-g-x-in-the-interval-0-x-lt-8-evaluate-g-6-

Question Number 84121 by Rio Michael last updated on 09/Mar/20

given that

g (x) = {\begin{cases} x + 2, if 0 ⩽ x < 2 \\ x^{2}, if 2 ⩽ x < 4 \end{cases}

is periodic of period 4 .

sketch the curve for g (x) in the interval

0 ⩽ x < 8

evaluate g (- 6) .

Commented by MJS last updated on 09/Mar/20

period 4 \Rightarrow g (x) = g (x + 4 z); z \in Z

\Rightarrow g (- 6) = g (- 6 + 4 \times 2) = g (2) = 2^{2} = 4

Commented by Rio Michael last updated on 09/Mar/20

thanks sir how about the graph

Commented by MJS last updated on 09/Mar/20

the graph in [0; 4 [is the same as in [4; 8 [

x g (x)

0 2

. 5 2.5

1 3

1.5 3.5

2 4

2.5 6.25

3 9

3.5 12.25

4 16 is not part of g (x) but the \lim_{x \to 4^{-}} g (x)

\Rightarrow the graph seems to reach it but it {doesn}^{'} t

mark the point (4 ∣ 16) with a “ \circ^{″}

4 2

4.5 2.5

\dots

8 16 same as (4 ∣ 16)

Commented by Rio Michael last updated on 10/Mar/20

thanks sir