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Lesson Worksheet: Variation Functions Mathematics

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

Q1:

Fill in the blank: When 𝑥 changes from 2 to 2.3, the variation function 𝑉() for 𝑓 becomes .

  • A𝑓(2.3)𝑓(2)
  • B𝑓(2)𝑓(2.3)
  • C𝑓(2.32)
  • D𝑓(22.3)

Q2:

Fill in the blank: If the function 𝑓𝑓(𝑥)=5𝑥3, then the variation function 𝑉()= at 𝑥=2.

  • A7
  • B5
  • C2
  • D5

Q3:

Determine the variation function 𝑉() for 𝑓(𝑥)=8𝑥5𝑥8 at 𝑥=1.

  • A𝑉()=811
  • B𝑉()=8+1122
  • C𝑉()=811
  • D𝑉()=8+11
  • E𝑉()=8+11

Q4:

If 𝑉() is the variation function for 𝑓(𝑥)=𝑥4𝑥+2, what is 𝑉(0.2) when 𝑥=8?

Q5:

Determine the variation function of 𝑓(𝑥)=𝑥cos at 𝑥=𝜋2.

  • A𝑉()=()sin
  • B𝑉()=()cos
  • C𝑉()=()sin
  • D𝑉()=()cos
  • E𝑉()=+𝜋2sin

Q6:

Determine the variation function 𝑉() of 𝑓(𝑥)=𝑒 at 𝑥=2.

  • A𝑉()=𝑒
  • B𝑉()=𝑒
  • C𝑉()=𝑒1
  • D𝑉()=𝑒1𝑒
  • E𝑉()=𝑒𝑒1

Q7:

Determine the variation function 𝑉() for 𝑓(𝑥)=𝑥+𝑎𝑥+17 at 𝑥=1. Additionally, find 𝑎 if 𝑉49=116.

  • A𝑉()=+2+𝑎, 𝑎=0.61
  • B𝑉()=+(2+𝑎), 𝑎=2.57
  • C𝑉()=+2+𝑎, 𝑎=0.28
  • D𝑉()=+(2+𝑎)+34, 𝑎=31.43

Q8:

Determine the variation function of 𝑓(𝑥)=𝑎𝑥sin at 𝑥=𝜋.

  • A𝑉()=𝑎sin
  • B𝑉()=𝑎+sin
  • C𝑉()=𝑎sin
  • D𝑉()=𝑎cos
  • E𝑉()=𝑎cos

If 𝑉𝜋2=1, find 𝑎.

Q9:

If the variation function of $f(x) = ax^2+bx$ at $x = d $ is $V(h) = ah^2+bh $, what is the value of $d$?

  • A$ -2 $
  • B$ 1 $
  • C$ -1 $
  • D$ 2 $
  • E$ 0 $

Q10:

Determine the variation function 𝑉() for 𝑓(𝑥)=𝑎𝑥+𝑏𝑥+2 at 𝑥=1, and, from 𝑉12=72 and 𝑓(1)=6, determine the constants 𝑎 and 𝑏.

  • A𝑉()=2𝑎𝑏, 𝑎=2, 𝑏=2
  • B𝑉()=𝑎(+2)+𝑏, 𝑎=2, 𝑏=2
  • C𝑉()=𝑎+(2𝑎+𝑏), 𝑎=2, 𝑏=2
  • D𝑉()=𝑎(+2)𝑏, 𝑎=2, 𝑏=2

This lesson includes 27 additional questions and 251 additional question variations for subscribers.

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