Question

its a scavenger hunt!
look carefully at the table and the relation represented in each cell.
search for the following relations. select all that apply.

1. which relations are not functions?
2. which relations map two different input values to the same output? when variables are used to describe a relation, the variable x represents the input and the variable y represents the output.
3. find a relation that is equivalent to $6 - (2x - y) = 17 - 3(x + 2) - 2x$. is this relation a function?
4. identify two representations below that show the same function.

a.
{0, 2, 1, 5, 14, 4}
{8, 1, 10, 4, 5, 11}
{5, 8, 12, 4, 9, 0}

b.
input: a, b, c, d, e
output: 1, 2, 3, 4, 4

c.
$y = 2x + 1$

d.
input: full name of a student in your algebra class
output: number of pets at the student’s home

e.
graph of a line

f.
$f(x) = 5 - x$

g.
{(banana, yellow), (apple, red), (peach, orange), (strawberry, red), (kiwi, green), (grape, purple)}

h.
input: a, b, c, d
output: □, ○, △, ☆

i.

x	y
1	3
2	5
3	7
4	9

j.
a clerk’s wage w is $15 for each hour worked h.

k.
graph of a line

l.
$|x| + |y| = 1$

Explanation:

Sub - Question 3

Step 1: Simplify the left - hand side of the equation

We start with the equation \(6-(2x - y)=17-3(x + 2)-2x\). First, simplify the left - hand side by distributing the negative sign: \(6-2x + y\).

Step 2: Simplify the right - hand side of the equation

Simplify the right - hand side: First, expand \(3(x + 2)=3x+6\). Then the right - hand side becomes \(17-(3x + 6)-2x=17-3x-6-2x\). Combine like terms: \((17 - 6)+(-3x-2x)=11-5x\).

Step 3: Set the simplified left - hand side equal to the simplified right - hand side and solve for y

We have \(6-2x + y=11-5x\). Add \(2x\) to both sides: \(6 + y=11-5x + 2x=11-3x\). Then subtract 6 from both sides: \(y=11-3x - 6=5-3x\).

Step 4: Determine if the relation is a function

A relation is a function if for every input \(x\) (in the domain), there is exactly one output \(y\). The equation \(y = 5-3x\) is a linear equation. For any real number \(x\) we plug in, we will get exactly one value of \(y\). So, it is a function.

Answer:

The equivalent relation is \(y = 5-3x\) (or \(f(x)=5 - 3x\)) and this relation is a function.