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Function problem

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1.) What is the range of the following function? 2.) What is the equation of a linear function that passes through the points (−5, 33) and (2, 5)?

3.) What is the equation of the following piece-wise function? 4.) Function g(x) is a transformation of f(x) . What is the equation of g(x) in termsof f(x)? Feb 7, 2018

#1
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1.    Range  =  [ -10, 0 )  U  [6, 13 ]

2.    (−5, 33) and (2, 5)

Slope  =   (33 - 5)  / ( -5 - 2)  =   28/ -7  =  - 4

Equation

y  = -4 ( x - -5) + 33

y  =  -4x - 20 + 33

y  =  -4x  + 13

4.   g(x)  is f(x)  shifted 3 units to the left and 6 units up  ...so...

g(x)    =   f(x + 3)  +  6   Feb 7, 2018
#2
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3.

y  =  (5/6) (x + 4) + 3   ⇒  (5/6)x + 10/3 + 3  ⇒  (5/6)x + 19/3

y  =  3

y = (2/7) (x - 5) + 6  ⇒  (2/7)x - 10/7 + 42/7  ⇒  (2/7)x + 32/7

So....a possible piece-wise function is

(5/6)x + 19/3         if   -10 ≤ x ≤ -4

y  =            3                         if     -4 < x  ≤ 5

(2/7)x  + 32/7        if   5 < x  ≤ 12   Feb 7, 2018