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Let g(x)=sqrt(x-2k),AA2klt=x<2(k+1), whe...

Let `g(x)=sqrt(x-2k),AA2klt=x<2(k+1),` where `k in ` integer. Check whether `g(x)` is periodic or not.

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`g(x) = sqrt(x-2k) AA 2k le x lt 2(k+1)` , where k is an integer.
`rArr" "g(x) ={{:(......,,),(......,,),(sqrt(x+2)",",, -2le x lt 0), (sqrtx",",, 0le x lt 2), (sqrt(x-2)",",, 2le x lt 4), (sqrt(x-4)",",, 4le x lt 6),(......,,),(......,,):}`
Function in each branch is part of parabolas lying above x-axis.
Graph of the function is as shown in the following figure.

From the graph `y= g(x)` is periodic with period 2.
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CENGAGE ENGLISH-GRAPHS OF ELEMENTARY FUNCTIONS -EXERCISES
  1. Let g(x)=sqrt(x-2k),AA2klt=x<2(k+1), where k in integer. Check whethe...

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  2. Draw the graph of y= (1)/((1//x)).

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  3. (a) Draw the graph of f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",,...

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  4. Sketch the regions which points satisfy |x+y| ge 2.

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  5. Sketch the region satisfying |x| lt |y|.

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  6. For a point P in the plane, let d1(P)a n dd2(P) be the distances of th...

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  7. Draw the graph of y= (x-1)/(x-2).

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  8. The following figure shows the graph of f(x) =ax^(2)+bx +c, then find ...

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  9. The entire graph of the equation y=x^2+k x-x+9 in strictly above the x...

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  10. If x^2+2a x+a<0AAx in [1,2], the find the values of a.

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  11. Draw the graph of f(x) = x|x|.

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  12. Draw the graph of the function: Solve |(x^2)/(x-1)|lt=1 using the grap...

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  13. Draw the graph of y = |x^(2) - 2x|-x.

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  14. Draw the graph of y = {{:(2^(x)",",, x^(2)-2x le 0 ),( 1+3.5 x- x^(2),...

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  15. Draw the graph of f(x) = |x-1|+ |2x-3|. Find the range of the functio...

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  16. Draw the graph of f(x) =y= |x-1|+3|x-2|-5|x-4| and find the values of ...

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  17. Find the set of real value(s) of a for which the equation |2x+3|+|2x-3...

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  18. Draw the graph of y= 2^(((|x|+x))/(x)).

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  19. Draw the graph of y= x ^((1)/(log(e)x)).

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  20. Find the number of solutions to the equation x+log(e)x=0.

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  21. Draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

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