Which piecewise relation defines a function?

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  see below

Step-by-step explanation:

The relation is a function only if it is single-valued for all values of x.

  A: doubly-defined at x = 4.

  B: doubly-defined at x = 2

  C: a function

  D: doubly-defined on the interval (-5, -4]

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions