Question

Which table represents a function? A 2-column table with 4 rows. The first column is labeled x with entries negative 3, 0, negative 2, 8. The second column is labeled y with entries negative 1, 0, negative 1, 1. A 2-column table with 4 rows. The first column is labeled x with entries negative 5, 0, negative 5, 6. The second column is labeled y with entries negative 5, 0, 5, negative 6. A 2-column table with 4 rows. The first column is labeled x with entries negative 4, negative 2, negative 2, 0. The second column is labeled y with entries 8, 2, 4, 2. A 2-column table with 4 rows. The first column is labeled x with entries negative 4, 3, 1, negative 4. The second column is labeled y with entries 2, 5, 3, 0.

Answer 1

Answer:

A 2-column table with 4 rows. The first column is labeled x with entries negative 5, 0, negative 5, 6. The second column is labeled y with entries negative 5, 0, 5, negative 6

Step-by-step explanation:

Given table as ;

x                         y

-5                      -5

0                        0

-5                       5

6                        -6

A function is a law that defines a relationship between a variable(Independent) and another variable (dependent). This is expressed as y=f(x)

Using the set of values given, you can plot them as coordinates (x,y) to view the graph and get first idea if its linear or not.

From the graph, you notice a linear pattern passing through the origin(0,0) with only one outlier (-5,5)

A linear function can be written  as y=mx+c where m is the gradient and c is the y-intercept which is our case ,c=0

Finding m using the other points apart from (-5,5) you notice a gradient of, m= -1

For example taking points (0,0) and (6,-6) m=change in y values/change is x values

m=-6-0/6-0 = -6/6 =-1

For points (-5,5) and (6,-6) , m= -6-5/6--5 = -11/11 = -1

Finding the equation of the function taking m=-1 and points; (6,-6) (x,y)

y--6/x-6 = -1

y+6/x-6 = -1

y+6=-1(x-6)

y+6=-1x+6

y= -1x -----Equation of the function, hence this table represent a linear function.