Question

A function is a rule that assigns each value of the independent variable to exactly one value of the dependent variable. True or False

Answer 1

Let me define the term function first, A function is a rule or mapping such that each value in the domain called preimage has unique image in range.

For example , S={(1,2),(3,5)(6,5)(4,3)} is a function but two Same values in the Range have different Pre-images.

The ordered pair (x,y) has x= Domain , and y= Range.

If, y=x +5, here x is an independent variable and y is a dependent variable. For different x values ,we get unique y value.

So, Yes the Statement is true that , A function is a rule that assigns each value of the independent variable to exactly one value of the dependent variable.

Answer 2

The answer is true
Let's imagine that we have the following function function:

`y = x ^ 2`
We have to:
Independent variable: x
Dependent variable: y
For x = -1:

`y = (- 1) ^ 2 = 1`
For x = 1:

`y = (1) ^ 2 = 1`
We observe that the independent variable can only obtain one result.
Answer:
True