Tell whether if the following piecewise function is a continuous at a given point or not. (SHOW THE SOLUTION).

Question

Tell whether if the following piecewise function is a continuous at a given point or not. (SHOW THE SOLUTION).

3. at x = 5

x² - 3 if x ≥ 5

4x + 2 if x < 5

Answer 1

x^2-3 = 5^2-3 = 25-3 = 22

4x+2 = 4(5)+2 = 20+2 = 22

at x=5 the stepwise function is continuous

x^2-3 is an upward openiing parabola

4x+2 is an unpward sloping straight line

x^2-3=4x+2

x^2 -4x -5 = 0

(x-5)(x+1) = 0

x-5 =0

x=5

the graphs meet at x=5, with no point of discontinuity