## Big Ideas Math Algebra 1 Student Journal 1st Edition Chapter 3 Graphing Linear Functions

**Page 59 Exercise 2 Answer**

**Given:-** {(0,8),(1,8),(2,8),(3,8)}

We have to determine whether each relation represents a function.

We can see that every element of the domain is connected with exactly one element of the codomain.

Therefore, the given relation is a function.

The relation {(0,8),(1,8),(2,8),(3,8)} is a function.

**Read and Learn More Big Ideas Math Algebra 1 Student Journal 1st Edition Solutions**

**Given:-** {(8,0),(8,1),(8,2),(8,3)}

We have to determine whether each relation represents a function.

We can see that one element of the domain is connected with more than one element of the codomain which contradicts the definition of the function.

Therefore, the given relation is not a function.

The relation {(8,0),(8,1),(8,2),(8,3)} is not a function.

**Given:-** {(1,8),(2,9),(3,10),(3,11)}

We have to determine whether each relation represents a function.

We can see that one element {3} of the domain is connected with more than one element of the codomain which contradicts the definition of the function.

Therefore, the given relation is not a function.

The relation {(1,8),(2,9),(3,10),(3,11)} is not a function.

**Given:-** {(1,6),(2,4),(5,4),(5,5),(7,5),(7,8)}

We have to determine whether each relation represents a function.

We can see that one or more elements ({5,7}) of the domain are connected with more than one element of the codomain which contradicts the definition of the function.

Therefore, the given relation is not a function.

The relation {(1,6),(2,4),(5,4),(5,5),(7,5),(7,8)} is not a function.

**Given:-** {(−2,5),(−1,8),(0,6),(1,6),(2,7)}

We have to determine whether each relation represents a function.

We can see that every element of the domain is connected with exactly one element of the codomain.

Here, the range is the same for the two elements of the domain, which is not a problem.

Therefore, the given relation is a function.

The relation {(−2,5),(−1,8),(0,6),(1,6),(2,7)} is a function.

**Given:-** {(−2,0),(−1,0),(−1,1),(0,1),(1,2),(2,2)}

We have to determine whether each relation represents a function.

We can see that one or more elements ({−1}) of the domain are connected with more than one element of the codomain which contradicts the definition of the function.

Therefore, the given relation is not a function.

The relation {(−2,0),(−1,0),(−1,1),(0,1),(1,2),(2,2)} is not a function.

**Given:-** Each radio frequency x in a listening area has exactly one radio station y.

We have to determine whether each relation represents a function.

We can see that every element of the domain is connected with exactly one element of the codomain.

Therefore, the given relation is a function.

The relation “Each radio frequency x in a listening area has exactly one radio station y.” is a function.

**Given:-** The same television station can be found on more than one channel.

We have to determine whether each relation represents a function.

We can see that one or more elements of the domain are connected with more than one element of the codomain which contradicts the definition of the function.

Here, domain means television and range is for channels.

Therefore, the given relation is not a function.

The relation “The same television station can be found on more than one channel.” is not a function.

**Given:-** x=2

We have to determine whether each relation represents a function.

We can see that one or more elements of the domain are connected with more than one element of the codomain which contradicts the definition of the function.

Here, an element {2} of the domain is connected with every element of the range.

Therefore, the given relation is not a function.

The relation x=2 is not a function.

**Given:-** y=2x+3

We have to determine whether each relation represents a function.

We can see that every element of the domain is connected with exactly one element of the codomain.

Moreover, a linear equation is always a function.

Therefore, the given relation is a function.

The relation y=2x+3 is a function.

**Page 60 Exercise 3 Answer**

**Given:-** A function.

We have to write some examples of relations which are functions.

In the functions, each element of the domain must be connected with exactly one element of the range.

Some examples of functions are

y=x

y=mx+c

{(1,1),(1.4,1),(2,2),(2.4,2)}

y=4

The examples of relations which are functions are

y=x

y=mx+c

{(1,1),(1.4,1),(2,2),(2.4,2)}

y=4

**Given:-** A function.

We have to write some examples of relations that are not functions.

In the functions, each element of the domain must be connected with exactly one element of the range.

Some examples of relations that are not functions

x=9

{(1,1),(1,1.4),(2,2),(2,2.4)}

{(1,1),(2,1),(3,1),(5,1)}

The examples of relations that are not functions are.

x=9

{(1,1),(1,1.4),(2,2),(2,2.4)}

{(1,1),(2,1),(3,1),(5,1)}

**Page 63 Exercise 1 Answer**

**Given:-** {(−2,4),(0,4),(1,5),(−2,5)

We have to determine whether each relation represents a function.

We can see that one or more elements of the domain are connected with more than one element of the codomain which contradicts the definition of the function.

Here, an element {−2} of the domain is connected with more than one element of the range.

Therefore, the given relation is not a function.

The relation {(−2,4),(0,4),(1,5),(−2,5)} is not a function.

**Page 63 Exercise 2 Answer**

**Given:-** {(0,3),(1,1),(2,1),(3,0)}

We have to determine whether each relation represents a function.

We can see that every element of the domain is connected with exactly one element of the codomain.

Therefore, the given relation is a function.

**Page 63 Exercise 4 Answer**

**Given:-** graph of y=x^{2}

We have to determine whether each relation represents a function.

We can see that every element of the domain is connected with exactly one element of the codomain.

Moreover, a quadratic equation in two variables is always a function.

Therefore, the given relation is a function.

The relation y=x^{2} is a function.

**Page 63 Exercise 5 Answer**

**Given:-** A graph whose ordered pairs are {(1,4),(2,4),(0,4),(3,3),(4,3),(5,3)}

We have to find its domain and range.

The domain is the set of elements on the left side of the ordered pairs, i.e.,

{0,1,2,3,4,5}

The range is the set of elements on the right side of the ordered pairs, i.e.,

{3,4}

The domain and the range of {(1,4),(2,4),(0,4),(3,3),(4,3),(5,3)} are {0,1,2,3,4,5} and {3,4} respectively.

**Page 63 Exercise 6 Answer**

**Given:-** A graph whose equation is given by y=|x|

We have to find its domain and range.

From the graph, we can see that

The domain is [−3,3]

And the range is [0,3].

The domain and the range are [−3,3] and [0,3] respectively.

**Page 63 Exercise 7 Answer**

**Given:-** y=12x

We have to tell the independent and dependent variables.

Here, y represents the number of pages of text a computer printer can print and x represents time.

The function is y=12x

Here, x i.e., time is an independent variable

And y, i.e., the number of pages that can print is a dependent variable.

The number of pages that can print is a dependent variable that depends upon an independent variable time.