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UNIT1-CHALLENGE 1.2: Functions and Their Graphs
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UNIT1-CHALLENGE 1.2: Functions and Their Graphs

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1 — What Is a Function?

1. What is meant by the term “function”?
A function in mathematics means that a single input leads to a single output. Mathematically, the output is the result of the input(s) used.

Determine if a given relation is also a function.

Solving Functions-and-Their-Grapghs

Which of the following is a function?

A.)

y squared equals x squared minus 5 x plus 3

B.)

y squared plus 7 equals 9 x

C.)

x squared plus y squared equals 49

D.)

x squared equals y minus 7

Which of the following is a function?

  • A.)

    y squared equals x squared minus 4

  • B.)

    y to the power of blank subscript 2 end exponent plus 2 equals 4 x

  • C.)

    2 x minus 3 y equals 18

  • D.)

    x squared plus y squared equals 36

    Which of the following is a function?

    • A.)

      2 x minus 3 y squared equals 18

    • B.)

      y squared plus 2 equals 7 x squared

    • C.)

      x cubed plus 2 y equals 54

    • D.)

      short dash x to the power of 4 plus y squared equals 3 x squared minus 5

      Functions

      Some of the functions we have covered are given below.

      When to use a situation formula:
      A equals L W Input are L = Length and W = Width
      The area is the value of the variable A.
      The is a direct result of L and W.

      Solving Functions-and-Their-Grapghs
      The perimeter of a square equals 4 times the side length.
      People define Perimeter (P) as the Output.
      Population is a function of sensors.
      The volume of a Right Circular Cylinder is V = πr squared x straight h Example: Given the radius (r) = 5 and height (h) = 6, the volume (V) is 50π
      Plugin: V = Null
      V relies on both r and h.

      Consider your calculator as an example of what a function is. Pressing the square root button results in the calculator computing the square root of the number input (if the input is 16, the calculator displays 4). Only a single value is returned by a calculator; this is the definition of a function.

      Functions
      There is a mapping from the set of inputs (x) to the set of outputs (y), where the inputs only go to one output.

      Solution 

      Which of the following is a function?

      • A.)

        y squared equals x squared minus 5 x plus 3

      • B.)

        y squared plus 7 equals 9 x

      • C.)

        x squared plus y squared equals 49

      • D.)

        x squared equals y minus 7

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