Mathematics

Question

Between x = 0 and x = 1, which function has a smaller average rate of change than y = 3x ? A) y = 8x + 2 B) y = 3x + 2 Eliminate C) y = 2x

2 Answer

  • The average rate of change of a function over a closed interval [a,b] is given with : f(b)-f(a)/(b-a).

    The interval in our case is [0,1]. The average rate of change fot the function y=3x is:

    (3*1-3*0)/(1-0)=3/1=3

     

    We will calculate the average rate of changes of all listed functions:

    A)    y = 8x + 2

    (8*1+2) – (8*0+2)/(1-0)=(10-2)/1=8/1=8

    B)     y = 3x + 2

    (3*1+2) – (3*0+2)/1=5-2=3

    C)    y = 2x

    (2*1) – (2*0)/1=2

     

    So, smaller average rate of change has the function y=2x.

  • Answer:

    option C has smallest rate of change

    Step-by-step explanation:

    given points  x = 0 and x = 1

    hence putting value in equation y = 3x

                        y = 0   and  y = 3

    rate of change of  = [tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-0}{1-0} = 3[/tex]

    from equation A) y = 8 x + 2

    at x = 0   y = 2            and    at x = 1   y = 10

    rate of change =   [tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{10-2}{1-0} =8[/tex]

    B) y = 3 x + 2

    at x = 0   y = 2            and    at x = 1   y = 5

    rate of change =   [tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-2}{1-0} =3[/tex]

    C) y = 2 x

    at x = 0   y = 0            and    at x = 1   y = 2

    rate of change =   [tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-0}{1-0} =2[/tex]

    hence, option C has smallest rate of change

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