Lesson Worksheet: Understanding Functions Mathematics

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In this worksheet, we will practice defining and evaluating functions and finding the roots and the maximum or minimum of quadratic functions.

Q1:

If 𝑓(𝑥)=5𝑥+7, evaluate 𝑓(−1).

Q2:

Given that 𝑓(𝑥)=𝑥+3 and 𝑔(𝑥)=−2𝑥+3, find the value of 𝑓(1)+𝑔(2).

Q3:

If 𝑓(𝑥)=2𝑥+4 and 𝑔(𝑥)=2−𝑥, calculate 𝑓(−1)𝑔(0).

Q4:

Find all of the roots of the function 𝑓(𝑥)=𝑥+5𝑥+4.

  • A𝑥=1, 𝑥=4
  • B𝑥=−1, 𝑥=−3
  • C𝑥=1, 𝑥=−4
  • D𝑥=−1, 𝑥=−4
  • E𝑥=−1, 𝑥=4

Q5:

Find the roots of the cubic function 𝑓(𝑥)=𝑥−𝑥−2𝑥.

  • A𝑥=−1, 𝑥=0, and 𝑥=−2
  • B𝑥=−1, 𝑥=1, and 𝑥=2
  • C𝑥=−1, 𝑥=0, and 𝑥=2
  • D𝑥=1, 𝑥=0, and 𝑥=−2
  • E𝑥=1, 𝑥=0, and 𝑥=2

Q6:

Find all the real roots of the function 𝑓(𝑥)=𝑥−𝑥−12.

  • A𝑥=4, 𝑥=3
  • B𝑥=2, 𝑥=3
  • C𝑥=4, 𝑥=−3
  • D𝑥=2, 𝑥=−3
  • E𝑥=2, 𝑥=−2

Q7:

If 𝑓(𝑥)=𝑥−2𝑥 and 𝑔(𝑥)=16−2𝑥, find all real values of 𝑥 such that 𝑓(𝑥)=𝑔(𝑥).

  • A𝑥=16, 𝑥=0
  • B𝑥=4, 𝑥=−4
  • C𝑥=16, 𝑥=−16
  • D𝑥=4, 𝑥=0
  • E𝑥=−4, 𝑥=0

Q8:

If 𝑓(𝑥)=3𝑥+4𝑥 and 𝑔(𝑥)=𝑥−4𝑥−6, find all of the real values of 𝑥 such that 𝑓(𝑥)=𝑔(𝑥).

  • A𝑥=−3, 𝑥=−1
  • B𝑥=3, 𝑥=−1
  • C𝑥=−3, 𝑥=1
  • D𝑥=3, 𝑥=1
  • E𝑥=−3, 𝑥=−2

Q9:

By writing the function 𝑓(𝑥)=𝑥+6𝑥+5 in the form (𝑥+𝑝)+𝑞, find the minimum output of the function.

Q10:

By writing the function 𝑓(𝑥)=𝑥−𝑥−34 in the form (𝑥+𝑝)+𝑞, find the minimum output of the function.

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