Question

Write a piecewise defined function for the graph​

Answer 1

Answer:

  a) f(x) = {-3/5(x-2)-2, x≤2; 5/2(x-2)-2, x>2}

  b) f(x) = (-1/5(x-2)-1, x≤2; 1/2(x-4)+3, x>2}

Step-by-step explanation:

a) You can count grid squares on the graph and determine the slope of the left section is ...

  rise/run = -3/5

and the slope of the right section is ...

  rise/run = 5/2

The point-slope equation of a line is convenient to use for these. It tells you that a line with slope m through point (h, k) can have the equation ...

  y = m(x -h) +k

Point (2, -2) is on both lines, so the function can be defined as ...

  $\displaystyle f(x)=\left\{\begin{array}{ll}-\frac{3}{5}(x-2)-2&\text{for x\le 2 }\\\frac{5}{2}(x-2)-2&\text{for x>2 }\end{array}\right.$

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b) The slope of the left section is ...

  rise/run = 1/5

and the slope of the right section is ...

  rise/run = 1/2

The left section ends at point (2, -1), and the right section goes through point (4, 3). As above, we can use the point-slope equation of a line to write the equations of the pieces. Note that at x=2, the defined point is included in the left section.

  $\displaystyle f(x)=\left\{\begin{array}{ll}\frac{1}{5}(x-2)-1&\text{for x\le 2 }\\\frac{1}{2}(x-4)+3&\text{for x>2 }\end{array}\right.$