Question

Value Where The Rule For The Function Changes.
F(X)=(X²)-11x+23,X<-2),(-15x+19,X>=-2)

Answer 1

The value where the rule for the function changes occurs at x = -2.

Step-by-step explanation:

The function F(x) is defined in two separate pieces with different rules for different intervals. For x < -2, the function is expressed as F(x) = x² - 11x + 23. At x = -2, the function encounters a transition point to the next rule, which is defined for x ≥ -2 as F(x) = -15x + 19. To find the point where the rule for the function changes, we observe that the transition occurs precisely at x = -2. At this point, the function switches from the rule represented by the quadratic equation to the rule expressed by the linear equation.

The function is divided into two segments based on the value of x. For x < -2, the function is governed by the equation F(x) = x² - 11x + 23. For x ≥ -2, the function changes its rule to F(x) = -15x + 19. The point of transition is where the change from one rule to another occurs, which in this case is x = -2. This means that up to x = -2, the function behaves according to the quadratic equation rule, and from x = -2 onwards, it follows the linear equation rule. Hence, the critical value where the function's rule changes from the quadratic to the linear expression is at x = -2.