You were given the follow algorithm for a function f(x).

Question

Inverse Relations

1. Start with a number and add 2.
2. Take the result and multiple by 3.
3. Take the result and subtract 10.
4. Square the final number.

(Fill in the blank using the word bank)

1. Start with a number_________.
2. Take the result and____________.
3. Take the result and_____________.
4. Take the final number and____________.

Word Bank:

1. take the square root.
2. square it
3. multiple by 3
4. divide by 3
5. add 2
6. subtract 2
7. add 10
8. subtract 10

Answer 1

x add 2

x+2 multiply by 3

3(x+2) = 3x + 6 subtract 10

3(x+2) - 10 = 3x -4 square the result

[3(x+2)-10]^2= (3x-4)^2

= 9x^2 -24x + 16 which is a parabola

y = 9(x^2 - 8x/3 + 16/9) = 9(x-4/3)^2 which is an upward opening parabola with vertex (4/3,0) = minimum point

Answer 2

Logan, they tell you the answers. I've highlighted them for you. You just need to read.

1. Starts with a number (x) and add 2 ---> x+2
2. Take the result and multiply by 3 ---> 3(x+2)
3. Take the result and subtract 10 ---> 3(x+2) - 10
4. Square (it) the final number ---> [3(x+2) - 10]²

(Fill in the blank using the word bank)

1. Start with a number_________.
2. Take the result and____________.
3. Take the result and_____________.
4. Take the final number and____________.

In math symbology, the algorithm is f(x) = [3(x+2)-10]² = (3x-4)²