Function problem

Question

0

699

2

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)?

Guest Feb 7, 2018

CPhill · Answer 1 · 2018-02-07T02:17:19

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

CPhill · Answer 2 · 2018-02-07T03:08:20

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