Question

1. which table at the right represents the inverse of the table shown below?| x | y ||----|----|| 0 | 2 || 2 | 4 || 3 | 10 || 4 | 19 |option 1:| x | y ||----|----|| 0 | -2 || 2 | -4 || 3 | -10 || 4 | -19 |option 2:| x | y ||----|----|| 2 | 0 || 4 | 2 || 10 | 3 || 19 | 4 |option 3:| x | y ||----|----|| 0 | 2 || -2 | 4 || -3 | 10 || -4 | 19 |option 4:| x | y ||----|----|| 2 | 0 || 4 | -2 || 10 | -3 || 19 | -4 |2. use algebraic notation to show how to transform the green function to the purple function.a) $f(x + 2)$b) $f(x - 2)$c) $f(x) + 2$d) $f(x) - 2$

Explanation:

Step1: Find inverse of first table

To find the inverse of a function table, swap the \(x\) and \(y\) values of each ordered pair.
Original pairs: \((0,2), (2,4), (3,10), (4,19)\)
Inverse pairs: \((2,0), (4,2), (10,3), (19,4)\)

Step2: Match inverse to options

Compare the inverse pairs to the given tables. The top-right table matches these pairs.

Step3: Analyze function transformation

For the graph: The green function (lower V-shape) and purple function (upper V-shape) have the same slope, so it is a vertical shift. The purple function is 2 units above the green function. A vertical shift up by \(k\) is written as \(f(x)+k\), here \(k=2\).

Answer:

1. The inverse table is the top-right table:

x	y
4	2
10	3
19	4

1. c) \(f(x) + 2\)