Finding the Equation of a Greatest Integer Function You need: 1) A closed endpoint for the h,k 2) The vertical height (counter step height ‘a’) 3) The length of the step, to determine ‘b’ With the above you can determine the sign of ‘a’ and ‘b’ and find the case. Find the equation in standard form, y = a[b( x − h)] + k , of the greatest integer function given: The zeros of the function are ]− 1,2] and f(4.5)= -­‐2. Solution: Sketch first! (The blue ‘dot’ is the point f(4.5)=-­‐2) Therefore: ⎡ 1
⎤
y = 2 ⎢− (x − 2 )⎥
⎣ 3
⎦
or
⎡ 1
⎤
y = 2 ⎢− (x − 5)⎥ − 2
⎣ 3
⎦
Since, length = 3, (determined by the zeros) 1
3
1
3
b= (this will be -­‐ because it is case 2) a = 2 (information found by the provided point and zeros) Decreasing (information found by the provided point and the zeros) Case 2, so a + and b is -­‐.