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Assignment: Translating Functions Investigation

Jeremy is opening a savings account earning simple interest. He plans to deposit his $50 birthday money and leave the account alone until he goes to college. He will earn $5 per year in interest.

The function f(x) = 5x + 50 represents his account balance after x years.
The graph of this is shown.
(Check the first graph)

Part A (Check the second graph)
1. Graph the translation of the function up 10 units.
2. Give the coordinate rule for a translation up 10 units.
3. What does a translation of the function up 10 units mean in terms of Jeremy's savings?

Part B (Check the third graph)
1. Graph the translation of the function right 10 units.
2. Give the coordinate rule for translation right 10 units.
3. What does a translation of the function right 10 units mean in terms of Jeremy's savings?

Part C
1. Look at the translations, what characteristic of the graph stayed the same in each translation?

2. Look at the original graph and the graph of the translation right 10 units. What vertical translation of the graph in Part B would put the graph back to its original position? Explain how you determined this.

Assignment Translating Functions Investigation Jeremy is opening a savings account earning simple interest He plans to deposit his 50 birthday money and leave t class=
Assignment Translating Functions Investigation Jeremy is opening a savings account earning simple interest He plans to deposit his 50 birthday money and leave t class=
Assignment Translating Functions Investigation Jeremy is opening a savings account earning simple interest He plans to deposit his 50 birthday money and leave t class=

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calculista

Answer:

Part A)

1) The graph in the attached figure N 1

2) The coordinate rule is (x,y) -----> (x,y+10)

3) The translation of the function up 10 units means that the initial deposit is $60 instead of $50

Part B)

1) The graph in the attached figure N2

2) The coordinate rule is (x,y) -----> (x-10,y)

3) The translation of the function right 10 units means that the initial deposit is equal to $10

Part C)

1) In each translation, the slope is the same (m=5) are parallel lines

2) The vertical translation would be up 40 units

Step-by-step explanation:

we have

[tex]f(x)=5x+50[/tex]

where

f(x) --> represents Jeremy's account balance

x ---> the time in years

Part A)

The translation of the function is up 10 units.

The rule of the translation is equal to

(x,y) -----> (x,y+10)

so

The new function will be

[tex]f(x)=5x+50+10[/tex]

[tex]f(x)=5x+60[/tex]

The graph in the attached figure N 1

The translation of the function up 10 units means that the initial deposit is $60 instead of $50

Part B)

The translation of the function is right 10 units.

The rule of the translation is equal to

(x,y) -----> (x-10,y)

so

we have

[tex]f(x)=5x+60[/tex] ----> function Part A

The new function will be

[tex]f(x)=5(x-10)+60[/tex]

[tex]f(x)=5x+10[/tex]

The graph in the attached figure N 2

The translation of the function right 10 units means that the initial deposit is equal to $10

Part C)

1. Look at the translations, what characteristic of the graph stayed the same in each translation?

In each translation, the slope is the same

The slope m is equal to m=5  

Are parallel lines

2. Look at the original graph and the graph of the translation right 10 units. What vertical translation of the graph in Part B would put the graph back to its original position?

we have

[tex]f(x)=5x+10[/tex]

The vertical translation would be up 40 units

The rule of the translation is equal to

(x,y) -----> (x,y+40)

so

The new function will be

[tex]f(x)=5x+10+40[/tex]

[tex]f(x)=5x+50[/tex]

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The translation of the original linear function, f(x) = 5·x + 50, gives the

following values;

Part A:

  1. Please find attached the graph of the function  f(x) + 60 = 5·x + 60, which is the graph of the original function translated up 10 units
  2. (x, y + 10)
  3. The account value is increased by $10

Part B:

  1. Please find attached the graph of the function translated to the right by 10 units
  2. (x + 10, y)
  3. The number of years the interest is applied is increased by 10

Part C:

  1. The slope of the graph stayed the same in each translation
  2. The vertical translation is 50 units

Which method can be used to make the given translations?

The function for the amount of money in the account is; f(x) = 5·x + 50

Part A

1. The graph of the translation of the above function up 10 units gives

the function;

f(x) + 10 = 5·x + 50 + 10 = 5·x + 60

f(x) + 10 = 5·x + 60

Please find attached the graph of the function translated up 10 units created with MS Excel

2. The coordinate rule for a translation up 10 units is; [tex]\underline{(x, \ y + 10)}[/tex]

3. The meaning of the translation up 10 units means that amount in the

account at a point in time is increased by $10

Part B;

1. The function, f(x) = 5·x + 50, translated 10 units to the right gives;

f(x + 10) = 5·(x + 10) + 50 = 5·x + 100

Please find attached the graph of the function translated right 10 units created with MS Excel

2. The coordinate rule is (x, y) [tex]\underrightarrow{T_{(10, \ 0)}}[/tex] [tex]\underline{(x + 10, \ y)}[/tex]

3. A translation of the function to the right, means that the point in time at

which the graph starts, the account balance is $100, such that Jeremy

the time the interest is applied is 10 years longer, than the original time

added to the number of years in the given function, f(x) = 5·x + 50

Part C

1. The characteristic of the graph that stays the same is the slope

2. The vertical translation in the graph of the translation right 10 units

compared to the original graph is 50 units.

Learn more about the graphs of linear functions here:

https://brainly.com/question/3469338

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