A group of students were discussing whether the relationship on the graph
is a function.

A function is a relationship that maps the elements of a set, the domain, into elements of another set, the range.

The restriction that we have for functions is: The elements on the domain can be mapped into only one element in the range.

Then if:

f(x1) = y1

and

f(x1) = y2

where y1 is different than y2

f(x) is not a function.

Now, in the graph you can see a region where both lines overlap, then for some values of x we have two possible values of y, this means that the graph does not represent a function.

Then:

Ed: He is incorrect because we can have different values in the domain mapped into the same value in the range (like in the case of a line y = b, where we have all the elements in the domain mapped into the same element in the range, b)

Debra: There is something called piecewise functions, that are functions of this type, formed by different pieces.

Alejandro: He is correct.

Antoine: Not because you can write an equation means that the relation is a function. You can write an equation for a circle, but it will not be a function.

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

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.