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2 years ago

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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 .

2 answers:

IrinaVladis [17]2 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]2 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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Answer:

β = (-0.19 dB).

Step-by-step explanation:

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The intensity of a monster truck is converted into per square meter as follows:

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2 years ago

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1. Write 3,876,943,000 using scientific notation.

Sunny_sXe [5.5K]

Answer:

3.876943x10^9

7.317x10^-4

Step-by-step explanation:

3,876,943,000

Put the decimal at the end

3,876,943,000.

Move it so only 1 number is before the decimal

3.876943000

We moved it 9 places, so that is the exponent

We moved it to the left, so the exponent is positive

The three zeros at the end can be dropped because they are the last numbers to the right of the decimal

3.876943x10^9

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Move it so only 1 number is before the decimal

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We moved it to the right, so the exponent is negative

The four zeros at the left can be dropped because they are the last numbers to the left of the whole number

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Time taken by Ria to paint a room = 4 hours

Time taken by Destiny to paint a room = 6 hours

If they work together, they complete 1 job. So,

$\frac{1x}{4}+\frac{1x}{6}=1$

The LCD of 4 and 6 is 12

$\frac{3x+2x}{12}=1$

$\frac{5x}{12}=1$

$5x=12$

$x=\frac{12}{5}$

Hence, both of them can paint the room in $\frac{12}{5}$ hours or 2.4 hours.

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Answer:

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Step-by-step explanation:

To solve this problem we must pay attention to the following data supplied:

- f It is the number of figurines that remain to be painted.

- t amount of time, in minutes, that Colin spends painting

- Colin takes 20 minutes painting each figurines.

- After painting 60 min, he still has 9 figurines left. f (60) = 9

If he takes 20 minutes painting 1, it means that in 60 minutes he has painted 3 and he has 9 left.

Then, at the beginning he has 9 +3 figurines to be painted.

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With these two points we can find the function:

If m is the slope of the line, then:

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Where by definition $c = f(0) = 12$

Finally the formula is:

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