## New Functions from Old:Scaled and Shifted Functions exercises to accompany Calculus Applied to the Real World

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Everything for Calculus
Everything for Finite Math
Everything for Finite Math & Calculus
Utility: Function Evaluator & Grapher
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In each of the following, first sketch the select the graph of the given function, then select the graph below that corresponds to your sketch.
Note: Clicking on a graphic gives feedback for odd-numbered exercises only.

 1 $f(x) = \frac {1}{x + 2}$ 2 $f(x) = \frac {1}{x+ 1}$
Graph of $f(x)$ (Select One)

 3 $f(x) = (x+1)^2$ 4 $f(x) = (x+3)^2$

Graph of $f(x)$ (Select One)

 5 $f(x) = \frac {1}{x+ 1}-1$ 6 $f(x) = \frac {1}{x+ 1}+2$

Graph of $f(x)$ (Select One)

 7 $f(x) = (x-2)^{2} + 1$ 8 $f(x) = (x-2)^{2} - 2$

Graph of $f(x)$ (Select One)

 9 $f(x) = \|2x + 2\|$ 10 $f(x) = 2\|x + 2\|$

Graph of $f(x)$ (Select One)

 11 $f(x) = 2\|-x + 1\|$ 12 $f(x) = \|-2x + 1\|$

Graph of $f(x)$ (Select One)

Exercises 13 through 22 involve modifications of the graph of $f(x) = x^2$. In each case, sketch the graph and say what scaling or shifting procedure was used. (For instance "the graph was shifted 10 units to the right.")

 13. $g(x) = (x - 1)^2$ Answer for 13 14. $h(x) = (2x)^2$ 15. $s(x) = \left(\frac {1}{2} x \right)^2$ Answer for 15 16. $l(x) = (x + 2)^2$ 17. $m(x) = 2 + x^2$ Answer for 17 18. $n(x) = x^{2} - 1$ 19. $r(x) = 3x^2$ Answer for 19 20. $s(x) = \frac {x^2} {3}$ 21. $t(x) = 2(x-1)^2 - 1$ Answer for 21 22. $u(x) = 0.5(x + 2)^2$

Exercises $23-30$ are based on the functions $f(x) = (x)^1/2$ and $g(x) = |x|$. Sketch their graphs, and say what scaling or shifting procedure was used.

 23. $h(x) = -\sqrt{x - 2} + 1$ Answer for 23 24. $h(x) = \sqrt{-x - 1} + 1$ 25. $h(x) = -\sqrt{- (x - 2)} + 1$ Answer for 25 26. $h(x) = 1 -\sqrt{(-x - 1)}$ 27. $m(x) = -\|2x + 2\|$ Answer for 27 28. $m(x) = -\|2 - x\|$ 29. $r(x) = -2\|x + 2\|$ Answer for 29 30.$r(x) = -2\|3x + 1\|$

In Exercises $31-40$, give an equation for the function f whose graph is given.

Applications

40. Cost Functions Suppose that fixed costs were to rise by 10,000.$Exactly how would the new cost function be related to C? How would their graphs be related? 41. Cost Functions Suppose that$D(x)$represents the cost to manufacture$x$more than$1,000$items. Exactly how are$D$and$C$related? How are their graphs related? Answer 42. Cost Functions Suppose that$D(x)$represents the cost, in thousands of dollars, to manufacture$x$items. Exactly how are$D$and$C$related? How are their graphs related? 43. Cost Functions Suppose that$D(u)$represent the cost to manufacture$u$hundreds of items. Exactly how are$D$and$C\$ related? How are their graphs related?