Lesson Worksheet: Understanding Functions Mathematics

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


If 𝑓(𝑥)=5𝑥+7, evaluate 𝑓(1).


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


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


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


Find the roots of the cubic function 𝑓(𝑥)=𝑥𝑥2𝑥.

  • 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


Find all the real roots of the function 𝑓(𝑥)=𝑥𝑥12.

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


If 𝑓(𝑥)=𝑥2𝑥 and 𝑔(𝑥)=162𝑥, 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


If 𝑓(𝑥)=3𝑥+4𝑥 and 𝑔(𝑥)=𝑥4𝑥6, 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


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


By writing the function 𝑓(𝑥)=𝑥𝑥34 in the form (𝑥+𝑝)+𝑞, find the minimum output of the function.

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