Mathematics High School

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 grab it and its parent function y=0.5^x on the same axes
The parent function y=0.5^x is _____ across its domain because its base b is such that

Answers

Answer 1

First box is: decreasing

Second box: 0< b< 1

Third box: Up

Fourth box: Right

Answer 2

The parent function y=0.5^x is decreasing across its domain because its base b is such that (0<b<1) and function shifts it 8 units up and 5 units right.

What is translation of a function?

Translation of a function is shifting the function from its original place in the graph.

Types of translation -

Horizontal shift- Let the parent function is f(x). Thus by replacing parent function with f(x-b) shifts the graph b units right and by replacing parent function with f(x+b) shifts the graph b units left.Vertical shift- Let the parent function is f(x). Thus by replacing parent function with f(x)+c shifts the graph c units down and by replacing parent function with f(x)-c shifts the graph b units up.

The functions of the graph given in the problem as,

[tex]f(x) = (0.5)^{x-5}+8[/tex]

The parent function of the graph is,

[tex]y=0.5^x[/tex]

In the parent function, the 5 units subtracted, and 8 units added outside the function. Thus, the function shifts the parent function 8 units up and 5 units right.

Thus, the parent function y=0.5^x is decreasing across its domain because its base b is such that (0<b<1) and function shifts it 8 units up and 5 units right.

Learn more about the transition of a function here;

https://brainly.com/question/626170

Related Questions

What is the missing reason for the 3rd step in the proof below?
A. If two lines are parallel, then alternate interior angles are congruent
B. Corresponding angles theorem
C. Vertical angles are congruent
D. If two lines are parallel, then alternate exterior angles are congruent

Answers

Answer:

The missing reason for the 3rd step in the proof below is;

C. Vertical angles are congruent

Step-by-step explanation:

In the two column proof, we have;

Statement   [tex]{}[/tex]            Reason

1. AB ║ CD   [tex]{}[/tex]           1. Given

2. ∠3 ≅ ∠7   [tex]{}[/tex]           2. Corresponding angles theorem

3. ∠7 ≅ ∠6   [tex]{}[/tex]           3. Vertical angles are congruent

4. m∠3 = m∠7   [tex]{}[/tex]      4. Definition of congruence    

m∠7 = m∠6

5. m∠3 = m∠6    [tex]{}[/tex]      5. Substitution

6. m∠3 ≅ m∠6    [tex]{}[/tex]     6. Definition of congruence

Vertical angles are the angles formed on the opposite sides of two straight lines when they cross each other

Other vertical angles in the diagram are;

1) ∠5 and ∠8

2) ∠1 and ∠4

3) ∠2 and ∠3

Find the midpoint between A (4, 2) and B (0, 6)

Answers

the midpoint would be (2,4)

Expand and simplify (x-3)(2x+1)(x+1)

Answers

2x³ - 3x² - 8x -3---------------------------

Step-by-step explanation:

(x-3)(2x+1)(x+1)

(2x² - 6x + x - 3)(x+1)

(2x² - 5x - 3) (x+1)

2x³ -5x² -3x + 2x² -5x - 3

2x³ - 3x² - 8x -3

---------------------------FOLLOW ME

a line is perpendicular to y=-2x+5 and intersects the point (-4,2). what is the equation of this perpendicular line?

Answers

Answer:

y = 1/2x + 4

Step-by-step explanation:

If the line is perpendicular to y = -2x + 5 then the new line has a slope of 1/2.

So solve for b: using y = mx + b

2 = 1/2(-4) + b

2 = -2 + b

4 = b

Put it all together

y = 1/2x + 4

What is the surface area of this right square pyramid?

with a width of 5cm and a height of 9cm


A.90cm squared

B.115cm squared

C.205cm squared

D.250cm squared

Answers

Answer:

it isn't 205 but my guess is its 115

need help i don't know of I got the the first problems rigth so just please tell me if I did and please answer second problem​

Answers

Answer: Question 1 is correct and Question 2 is 12 degrees :)

Step-by-step explanation: hope this helped!

For question one the answer is A and D. For question two the answer is A and B.

At the grand opening of a new store, every 9th customer will receive a balloon and every 12th customer will receive a $10 gift certificate. Which customer will be the first to get both a balloon and gift certificate?

Answers

Answer: 36th customer.

Step-by-step explanation: 36 is divisible by both 9 and 12, and is the least common multiple.


y = 2x - 6
y = - 4x + 3

Answers

Answer: x = 3/2, y = -3

hii pls help i’ll give brainliest if you give a correct answer

Answers

Answer:

east to west i think im not too sure

Answer:

north stars appear to move from east to west in the sky :)

Dino finds the line-of-best fit for the data set shown. What is the equation of Dino's line-of-best fit?

Answers

Answer:

y = 2.0x + 0.6

Step-by-step explanation:

Dino's data:

X _____ Y

1 ______ 1

2 ______5

3 ______6

4 _____ 10

5 _____ 13

6 _____ 13

7 _____ 14

8 _____ 16

9 _____ 18

10 _____21

Using the linear regression calculator, the line of best fit for the data is :

y = 2.0X + 0.6

Where ;

Slope = 2 ; intercept = 0.6

2y = 3/2 (16x+18) - 7

Answers

Answer:

y = 12x + 10

X = y/12 - 5/6

Answer:

y = 12x + 10

x = (y-10)÷12

Step-by-step explanation:

What is 4 & 1/2 ÷ 1/6?

Answers

Answer:

27

Step-by-step explanation:

4 1/2  = 9/5

9/2 : 1/6  =

9/2 x 6/1 =

(9x6) / (2x1) =

54/2  = 27

27 is the answer ;)

Calculate the volume.
Plz hurry!! 40 points in it!!

Answers

Answer:

tell me the decimals number form

Step-by-step explanation:

my question is in the photo

Answers

Answer:

all the answers are there in safari can  just check it

Step-by-step explanation

Please help im desperate. :)​

Answers

Answer:

b is ya answer hope you have a blessed day

Step-by-step explanation:

Answer:

C undefined sorry im rushing

there are 72 boys and 90 girls on a math team for the next competition mr. Johnson would like to arrange all the students in equal rows with only girls or only boys in each row. What is the greatest number of students that can be in each row ​

Answers

the greatest number of students that can be in each row is 18 !!:)

Rewrite the following using distributive property

1. 24+20
2. 12+16
3. 36+81
4. 49+84
5. 99+36​

Thanks❤

Answers

Answer:

12+16

24+20

36+81

49+84

99+36

Is this correct?????

Answers

Answer:

yeah i think so

Step-by-step explanation:

Answer:

it is correct jbhsjsshsusuwwy

Combine the like terms for the following expressions -3+4b-6g+5-7b

Answers

Answer:

-3b-6g+2

Step-by-step explanation:

if you combine like terms, it would be -3b-6g+2

Write an equation of the line that passes through (1,2) and is parallel to the line y = -5x+4

Answers

Answer:

y =-5x + 7

Step-by-step explanation:

y = -5x + 4

Slope = -5

Parallel lines have same slope

Slope of the parallel line to this line = -5

(1 , 2)

y -y1 =m(x - x1)

y - 2 = -5(x - 1)

y -2 = -5x + 5

   y = -5x + 5 + 2

  y = -5x + 7

Show work, please
32 points!

Answers

Answer:

1.Equivalent

2.Equaivalent

3.Not Equivalent

4.Equivalent


What is the length of the missing leg?

Answers

4.5 is the answerrreee

Write the equation for an exponential function that triples ever year, x, when the original amount is 4.

Answers

Answer:

y = 4(3)^x

Step-by-step explanation:

Here, we want to write the exponential equation

From the question, we have the equation tripling in x value every year and the original amount is 4

The exponential equation is of the form;

y = a(b)^n

In this case;

a = 4 , b = 3 and n = x

So we have the equation as;

y = 4(3)^x

Plz help I’m need help

Answers

I can’t really help you too much with the graphing but what you do with ordered pairs is whatever is the first number (example for point A it’s -2) you go and find it on the horizontal line. Once you find it on the horizontal line you either go up or down the graph by how many units the second number is (4 so you would go up four in the graph) and then you plot the point
here you go, just put dot on it

Can you please solve this

Answers

Answer: [tex]\frac{2(x-7)}{5(x-3)(x-2)}[/tex]

Step-by-step explanation:

I'll do the fraction on the left, then the one on the right. Follow the screenshots below to help you out.

1. Use distributive property. The first of the images is me distributing all the values on the fraction on the left. Now I will do the ones on the left.

2. I used the same method. Now I will multiply the two.

3. [tex]\frac{2(x-7)}{5(x-3)(x-2)}[/tex]

hello please help thank you!

Answers

Answer:

BC ≈ 5.44 m

Step-by-step explanation:

Using the cosine ratio in the right triangle

cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] , that is

cos27° = [tex]\frac{BC}{6.1}[/tex] ( multiply both sides by 6.1 )

6.1 × cos27° = BC , then

BC ≈ 5.44 m ( to 3 significant figures )

Find the value of x in the triangle.
A right triangle has one angle with a measure of 54 degrees and the other angle measure of x degrees.
A. 126°
B. 234°
C. 36°
D. 144°

Answers

If it’s a right angle, then take 180 and subtract 90 and 54 from it. Whatever number you get it angle x.

Answer:

Agreed, the answer is 36

Step-by-step explanation:

Subtract 180-90=90-54=

36

There's your answer.

In a small library, there are 55 nonfiction books for every 99 fiction books. There are 130130 nonfiction books.

a. How many fiction books are there? Use paper to draw a model to support your answer.

​

​​

​There are
fiction books.​

​b. ​​​How many more fiction books are there than nonfiction books?

​There are
more fiction books than nonfiction books.

Answers

There re 234234 fiction books

The population of a small town, P, as a function of time, t, in years past 1940 is given below. P = 2,828 + 125t For which of the following years was the population of the town 8,453?

Answers

Answer:

Step-by-step explanation:

P = 2,828 + 125t

8,453 = 2,828 + 125t

5625 = 125t

t = 45

You didn't post the choices, hope that I can help you.

Answer:

Any year after 1985

Step-by-step explanation:

8453=2828+125t

5625=125t

45=t

1940+45=1985

A triangle has side lengths 24,143 and 145 is it a right triangle?

Answers

Answer:

yes  last one

Step-by-step explanation:

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