- For the first function, f(x) = x + 5 if x < -2 and f(x) = -4 if x ≥ -2:
- Graph the line y = x + 5 for all x-values less than -2. This is a straight line with slope 1 and y-intercept 5, but only draw it to the left of x = -2. At x = -2, do not include the point on this line; leave an open circle at (-2, 3).
- Graph the horizontal line y = -4 for all x-values greater than or equal to -2. This is a flat line at height -4. At x = -2, include the point on this line; place a solid dot at (-2, -4).
- The function has a jump discontinuity at x = -2 because the left-hand limit (approaching from the left) is 3, while the right-hand limit and the function value are both -4.
- For the second function, f(x) = 2x + 1 if x < 1 and f(x) = -2x + 3 if x ≥ 1:
- Graph the line y = 2x + 1 for all x-values less than 1. This is a straight line with slope 2 and y-intercept 1, but only draw it to the left of x = 1. At x = 1, do not include the point on this line; leave an open circle at (1, 3).
- Graph the line y = -2x + 3 for all x-values greater than or equal to 1. This is a straight line with slope -2 and y-intercept 3. At x = 1, include the point on this line; place a solid dot at (1, 1).
- The function has a jump discontinuity at x = 1 because the left-hand limit (approaching from the left) is 3, while the right-hand limit and the function value are both 1.
Parent Tip: Review the logic above to help your child master the concept of piecewise functions worksheet with answers.
