A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 10, negative 8, negative 6, negative 4, negative 2, 0. Which is an x-intercept of the continuous function in the table?

An x-intercept of the continuous function in the table is at (f(x) = 0) that is (x = 3) is the x-intercept of the continuous function given in the table and this can be determined by observing the table.

Given :

x                   f(x)

-2                  -10

-1                    -8

0                   -6

1                    -4

2                   -2

3                    0  

An x-intercept of the continuous function in the table is at (f(x) = 0) that is (x = 3) is the x-intercept of the continuous function given in the table.

An y-intercept of the continuous function in the table is at (x = 0) that is (f(x) = -6) is the y-intercept of the continuous function given in the table.

For more information, refer to the link given below:

link

Step-by-step explanation:

Given the table

..xy=f(x)

-2-10

-1-8

0-6

1-4

2-2

30

x intercept means that the value of x when y = f(x) = 0, it is the point where the graph pass through or cut the x axis

So, from the diagram, it is the last column,

F(x) = 0, then, x=3

Then, the x intercept is 3

Extra

Also, for y intercept, it is the point when x = 0 for this case the y intercept is -6/

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

b

step-by-step explanation: