The graph of f(x) that satisfies the condition of f(x)'s left sided limit at 2 being -4 and right sided limit at x = 2 being 0 is given by the first graph.
What is one-sided limit for function of single variable?
In rough terminologies, the limit from one side is when we only use one side of the function with respect to the considered point of interest (in input) to predict the value of the function at that point.
For this case, we need to find the graph of the function f(x) from the considered 4 graphs for which:
[tex]\lim_{x\rightarrow 2^{-}}f(x) = -4\\\\\lim_{x\rightarrow 2^{+}}f(x) = 0\\[/tex]
For the first graph, for the point x=2, on left from the point x = 2 lies a ray. If thats the function, we can hope that the function will continue having the same line to the right too, so the prediction for value of function on x = 2 is the value that line gives for y.
That is -4.
Thus, prediction of function from left of x = 2 is -4, or
[tex]\lim_{x\rightarrow 2^{-}}f(x) = -4[/tex]
Similar to that, from the right of the point 2, there is some yellow curve. That predicts that the function's value at point x = 2 should be 0 (the yellow curve seems like touching the x-axis where y = 0 at the point x=2.
Thus, we have:
[tex]\lim_{x\rightarrow 2^{+}}f(x) = 0\\[/tex]
So graph first is correctly pertaining such function f(x).
Second graph when refered, we see that if we predict value at x =2 from left, the yellow curve in the left will make us predict that the function would be 0, so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = 0[/tex]
Thus, its wrong graph.
Third graph when refered, we see that if we predict value at x =2 from left, the green line in the left will make us predict that the function would be -2 at x = 2 (see the green point in the third graph), so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = -2[/tex]
Thus, its wrong graph.
Similarly, for the fourth graph, we see that if we predict value at x =2 from left, the yellow curve in the left will make us predict that the function would be 0, so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = 0[/tex]
Thus, its wrong graph.
Thus, the graph of f(x) that satisfies the condition of f(x)'s left sided limit at 2 being -4 and right sided limit at x = 2 being 0 is given by the first graph.
Learn more about one-sided limits here:
https://brainly.com/question/23625942
#SPJ1
