What is "given b (x) = startabsolutevalue x + 4 endabsolutevalue?

The function "given b(x) = |x + 4|" represents the absolute value function in which the input value x is added to 4 and then the absolute value of the sum is taken. The absolute value function returns the distance of a number from zero on the number line, disregarding the sign.

For negative values of x, the function evaluates to |x + 4| = -(x + 4), which simplifies to -x - 4. For positive values of x, the function evaluates to |x + 4| = x + 4.

Overall, the function "b(x) = |x + 4|" has a sharp turn at the point x = -4, where the function changes from being downward-sloping to upward-sloping. The graph of this function is a V-shaped graph centered at x = -4.

This function is often used in mathematics and engineering to model situations where the result must always be positive or to represent changes in values that have a distinct breakpoint.