SOLUTION: Please help, my teacher just gives us the lessons to do as homework and does not explain anything. Algebra 1, page 47, #14. a. Write a rule for the function -- Input

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Question 96911: Please help, my teacher just gives us the lessons to do as homework and does not explain anything.
Algebra 1, page 47, #14.
a. Write a rule for the function -- Input - 0, 1, 2, 3 and Output - 0, .5, 2, 4.5
b. Find the value of y so that (1.5,y) is on the graph of the function.
Thanks!
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
a)

Start with the given relation:

Input Output
0 0

1 0.5

2 2

3 4.5

Rewrite 0.5 as 1/2 and 4.5 as 9/2

Input Output
0 0

1 1/2

2 2

3 9/2

Notice 0 can be written as 0/2 and 2 as 4/2

Input Output
0 0/2

1 1/2

2 4/2

3 9/2

So we can see that new output sequence is

, , ,

Notice how the numerators follow the sequence

0,1,4,9

which is the sequence of perfect squares. So the numerator can be described with the expression

So that means we get the function

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b)

To find f(x) when x=1.5 (or 3/2) plug in that value of x to find f(x)

Plug in

Square the numerator

Flip the second fraction and multiply

Multiply

So when ,

SOLUTION: Please help, my teacher just gives us the lessons to do as homework and does not explain anything. Algebra 1, page 47, #14. a. Write a rule for the function -- Input - 0, 1, 2, 3