Write a function with a zero of 1/2 . Explain how you know.

Simplest function is f(x) = 2x - 1

Step-by-step explanation:

When a function has a zero, simply put, that point is where the graph goes through the x-axis.  At this point, the y value is 0.

If a function has a 0 of 1/2, that translates to x = 1/2 and also (1/2, 0).  That means that y = 0 when x = 1/2.

If x = 1/2 and is a zero, then x - 1/2 = 0 and 2x - 1 = 0 (notice that y = 0 here and solving for x would get you right back to x = 1/2).

The simplest function with a zero of 1/2 is

f(x) = 2x - 1

You know it is true that the zero is 1/2 for two reasons.  First one is to set the right side equal to 0 and solve for x.

The second one is to graph the line y = 2x - 1 and see that it goes through the x axis at 1/2 where y = 0.

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