Question

Write the linear function f with the values f(1) = 1 and f(-3) = 17. (Note: Use f(x) instead of y.) Show work to get full credits.

Answers

  1. Given:

    f(1) = 1 and f(-3) = 17

    To find:

    The lines function f.

    Solution:

    If f(a) = b, it means the function f passes through (a,b).

    Here, f(1) = 1, it means the function f passes through (1,1).

    f(-3) = 17, it means the function f passes through (-3,17).

    If a linear function passes through two point (x_1,y_1)\text{ and }(x_2,y_2), then the equation of line is

    y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

    The linear function f passes through (1,1) amd (-3,17). So, the equation of linear function is

    y-1=\dfrac{17-1}{-3-1}(x-1)

    y-1=\dfrac{16}{-4}(x-1)

    y-1=-4(x-1)

    y-1=-4x+4

    Add 1 on both sides.

    y-1+1=-4x+4+1

    y=-4x+5

    Put y=f(x), to write in function notation.

    f(x)=-4x+5

    Therefore, required lines function is f(x)=-4x+5.

    Reply

Leave a Comment