Graph the piecewise function f(x) = {x + 5 if x <_ "-2" f(x) = { 2x + 3 if x > "-2"
Will the graph have any open endpoints? If yes, where?
A. Yes, at (-2,3) and (-2, -1).
B. Yes, at (-2, -1).
C. Yes, at (-2 3).
D. No, all endpoints are closed
The graph of the function f(x) = {x + 5 if x < -2, f(x) = 2x + 3 if x > -2, will have an open endpoint at x = -2.
Therefore, the correct answer is B. Yes, at (-2, -1).
Please explain
I apologize for the confusion in my previous response. I misunderstood the question.
Given the piecewise function f(x) = {x + 5 if x < -2, f(x) = 2x + 3 if x > -2, we need to consider the behavior of the function around x = -2 to determine if there are any open endpoints.
For x < -2, the function is defined as f(x) = x + 5. This means that the graph of the function will be a line with a slope of 1 and a y-intercept of 5.
For x > -2, the function is defined as f(x) = 2x + 3. This means that the graph of the function will be a line with a slope of 2 and a y-intercept of 3.
So, at x = -2, we need to check if the function has the same value from both sides.
For x < -2 (to the left of -2), f(x) = x + 5. If we plug in x = -2 into this equation, we get f(-2) = -2 + 5 = 3.
For x > -2 (to the right of -2), f(x) = 2x + 3. If we plug in x = -2 into this equation, we get f(-2) = 2(-2) + 3 = -1.
Since the value of the function from the left side of -2 (x < -2) is 3, and from the right side of -2 (x > -2) is -1, there is a discontinuity at x = -2. This implies that there is an open endpoint at x = -2.
Therefore, the correct answer is B. Yes, at (-2, -1).