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?
The graph of the piecewise function f(x) = {x + 5 if x ≤ -2, f(x) = { 2x + 3 if x > -2 can be divided into two separate parts.
For x ≤ -2, the function is f(x) = x + 5. This is a linear function with a slope of 1 and a y-intercept of 5. The graph will be a straight line passing through the point (-2, 3) and extending indefinitely downwards.
For x > -2, the function is f(x) = 2x + 3. This is also a linear function with a slope of 2 and a y-intercept of 3. The graph will be a straight line passing through the point (-2, -1) and extending indefinitely upwards.
Since both parts of the function extend indefinitely in their respective directions, the graph will have open endpoints. The open endpoint on the left side will be (-∞, -∞), and the open endpoint on the right side will be (∞, ∞).