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.

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

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

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

----> function Part A

The new function will be

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

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

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.