the absolute value function, ( f(x)=|x + 2| ), is shown. if the graph is reflected over the ( x )-axis, what…
the absolute value function, ( f(x)=|x + 2| ), is shown. if the graph is reflected over the ( x )-axis, what is the domain of the function? all real numbers all real numbers greater than or equal to 0 all real numbers greater than or equal to -2 all real numbers less than or equal to -2
Answer
Explanation:
Step1: Understand the effect of reflection over the x - axis
When a function (y = f(x)) is reflected over the (x) - axis, the new function is (y=-f(x)). For (f(x)=\vert x + 2\vert), the reflected function is (g(x)=-\vert x + 2\vert).
Step2: Recall the definition of domain
The domain of a function is the set of all possible input values ( (x) - values). For any absolute - value function of the form (y = a\vert x - h\vert+k) (in our case (y =-\vert x + 2\vert), where (a=-1), (h=-2), (k = 0)), there is no restriction on the values of (x) based on the algebraic form of the absolute - value function.
Step3: Analyze the domain
The original function (f(x)=\vert x+2\vert) has a domain of all real numbers (because we can substitute any real number for (x) into the expression (x + 2) and then take the absolute value). When we reflect the function (y = f(x)) over the (x) - axis to get (y=-f(x)), we are only changing the (y) - values (the output values). The reflection over the (x) - axis does not introduce any new restrictions on the (x) - values.
Answer:
all real numbers