Mathematical Applications: Distance, Midpoint, And Piecewise Functions

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Mathematical Applications: Distance, Midpoint, and Piecewise Functions A. 1. Find the distance between the points ( - 2,3) and (1, - 1). Answer: The equation to calculate the distance between the points (a,b) and (c,d) is d= √ ( 𝑎 − 𝑐 ) 2 + ( 𝑏 − 𝑑 ) 2 So the distance between the points ( - 2,3) and (1, - 1) is d= √ ( − 2 − 1 ) 2 + ( 3 − ( − 1 ) ) 2 = √ 3 2 + 4 2 =5 2. Find the midpoint of the line segment joining the points ( - 2,3) and (1, - 2) Answer: The midpoint of the points (a,b) and (c,d) is ( 𝑎 + 𝑐 2 , 𝑏 + 𝑑 2 ), so the midpoint of ( - 2,3) and (1, - 1) is ( − 2 + 1 2 , 3 − 1 2 ) = ( - 1/2,1) The midpoint is ( - 1/2,1) G. The function of f(x) is defined as: f(x) = 1. a. Find f(0), f(2), f(5) 0 is in the range 2 ≤ x < 1 , so f(0)= - 2*0+3=3 2 is in the range 1 ≤ x ≤ 2 , so f(2)= 5 5 is in the range x > 2 , so f(5)= 5^2+2=27 b. Determine the domain of f(x) The domain is ( - ∞,∞) - 2x+3 if - 2 ≤ x < 1 5 if 1 ≤ x ≤ 2 x^2+2 if x > 2
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