Worksheet: Variation Functions

In this worksheet, we will practice evaluating the variation function at a point for a given function.

Q1:

Determine the variation function 𝑉 ( ) for 𝑓 ( 𝑥 ) = 𝑎 𝑥 + 𝑏 𝑥 + 2 at 𝑥 = 1 , and, from 𝑉 1 2 = 7 2 and 𝑓 ( 1 ) = 6 , determine the constants 𝑎 and 𝑏 .

  • A 𝑉 ( ) = 𝑎 ( + 2 ) 𝑏 , 𝑎 = 2 , 𝑏 = 2
  • B 𝑉 ( ) = 𝑎 ( + 2 ) + 𝑏 , 𝑎 = 2 , 𝑏 = 2
  • C 𝑉 ( ) = 𝑎 + ( 2 𝑎 + 𝑏 ) , 𝑎 = 2 , 𝑏 = 2
  • D 𝑉 ( ) = 2 𝑎 𝑏 , 𝑎 = 2 , 𝑏 = 2

Q2:

Determine the variation function 𝑉 ( ) for 𝑓 ( 𝑥 ) = 4 𝑥 9 𝑥 + 9 at 𝑥 = 1 .

  • A 𝑉 ( ) = 4 + 2 8
  • B 𝑉 ( ) = 4 1
  • C 𝑉 ( ) = 4 +
  • D 𝑉 ( ) = 4
  • E 𝑉 ( ) = 4 +

Q3:

If 𝑉 is the variation function for 𝑓 ( 𝑥 ) = 𝑥 4 𝑥 + 2 , what is 𝑉 ( 0 . 2 ) when 𝑥 = 8 ?

Q4:

Determine the variation function 𝑉 ( ) for 𝑓 ( 𝑥 ) = 𝑥 + 𝑎 𝑥 + 1 7 at 𝑥 = 1 . Additionally, find 𝑎 if 𝑉 4 9 = 1 1 6 .

  • A 𝑉 ( ) = + ( 2 + 𝑎 ) 𝑎 = 2 . 5 7 ,
  • B 𝑉 ( ) = + 2 + 𝑎 𝑎 = 0 . 6 1 ,
  • C 𝑉 ( ) = + ( 2 + 𝑎 ) + 3 4 𝑎 = 3 1 . 4 3 ,
  • D 𝑉 ( ) = + 2 + 𝑎 𝑎 = 0 . 2 8 ,

Q5:

Determine the variation function 𝑉 ( ) for 𝑓 ( 𝑥 ) = 8 𝑥 5 𝑥 8 at 𝑥 = 1 .

  • A 𝑉 ( ) = 8 1 1
  • B 𝑉 ( ) = 8 + 1 1 2 2
  • C 𝑉 ( ) = 8 + 1 1
  • D 𝑉 ( ) = 8 + 1 1
  • E 𝑉 ( ) = 8 1 1

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