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Chapter 1: Q3B. (page 47)

Determine if each of the equations represents a function 4x=y+8.

Short Answer

Expert verified

The given relation 4x=y+8 is a function.

Step by step solution

01

Step 1. To find.

If the relation 4x=y+8 is a function.

02

Step 2. Explanation.

A relation will be a function if

  1. Every value in its domain has a unique value in its codomain.
  2. For every value of x, there is a unique value of y.
  3. For every value of x, there must be only one value of y.
03

Step 3. Calculation.

Putting x=0, 2, 3, 4 in 4x=y+8 and writing the values in the tabular form we have,

xy=4x–8
(x,y)
0y=4(0)–8=–8
(0,-8)
2y=4(2)–8=0
(2,0)
3y=4(3)–8=4
(3,4)
4y=4(4)–8=8
(4,8)

Or, the relation can be represented as:

R={0,−8,2,0,3,4….}

From these ordered pairs we see that, for each different value of x, there is the unique value of y. It means this ordered pair satisfies the definition of a function.

04

Step 4. Conclusion.

From the above relation, for each x value, there is always a y value. So, 4x=y+8 is a function.

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