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bixtya [17]
3 years ago
11

Use what you know about translations of functions to analyze the graph of the function f(x) = (0.5)x−5 + 8. You may wish to grap

h it and its parent function, y = 0.5x, on the same axes. The parent function y = 0.5x is across its domain because its base, b, is such that . The function, f, shifts the parent function 8 units . The function, f, shifts the parent function 5 units .

Mathematics
2 answers:
IrinaVladis [17]3 years ago
5 0

Answer:

The Translation is 5 units to the right and 8 units up

Step-by-step explanation:

* Lets talk about some transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

∵ The parent function is y = (0.5)^x

∵ f(x) = (0.5)^x - 5 + 8 after translation

- The x in the first function is (x - 5) in the second function

∴ There is a horizontal translation to the right 5 units

- the first function is (0.5)^x in the second function y = (0.5)^x - 5 + 8

∴ There is a vertical translation up 8 units

* The Translation is 5 units to the right and 8 units up

- Look to the attached graph to more understand

- The purple graph is y = (0.5)^x

- The black graph is f(x) = (0.5)^x-5 + 8

- To check the answer take a point from the y = (0.5)^x as (0 , 1), the

 image of this point on f(x) is (5 , 9)

-The point (0 , 1) is shifted 5 units to the right and 8 units up

∴ Its x- coordinate move from 0 to 5, y- coordinate move from 1 to 9

n200080 [17]3 years ago
4 0

Answer:

The parent function y = 0.5x is DECREASING  across its domain because its base, b, is such that 0<b<1.

The function, f, shifts the parent function 8 units UP .

The function, f, shifts the parent function 5 units RIGHT .

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Answers:

The z scores are approximately:

  • Care of Magical Creatures:  z = 0.333
  • Defense Against the Dark Arts:  z = 0.583
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From those scores, we can say:

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=====================================================

Further Explanation:

We'll need to convert each given score to a corresponding standardized z score.

The formula to use is

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where,

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Let's find the z score for the Care of Magical Creatures class

z = (x - mu)/sigma

z = (3.80 - 3.75)/(0.15)

z = 0.333 approximately

Repeat this process for the Defense Against the Dark Arts score.

z = (x - mu)/sigma

z = (3.60 - 3.25)/(0.60)

z = 0.583 approximately

And for the Transfiguration class as well

z = (x - mu)/sigma

z = (3.10 - 3.20)/(0.38)

z = -0.263 approximately

The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.

Now do the final class (Potions) to get this z score

z = (x - mu)/sigma

z = (2.50 - 2.90)/(0.75)

z = -0.533 approximately

This grade is below average as well.

----------------------------

To summarize, we have these z scores

  • Care of Magical Creatures:  z = 0.333
  • Defense Against the Dark Arts:  z = 0.583
  • Transfiguration:  z = -0.263
  • Potions: z = -0.533

Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.

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