Question

Which table of values can be represented by the function y=x+4 ?

Answer 1

The table of values represented by the function ( y = x + 4 ) is a set of ordered pairs where the y-coordinate is always 4 more than the x-coordinate.

Step-by-step explanation:

The given function ( y = x + 4 ) indicates that for any chosen value of ( x ), the corresponding ( y )-value is obtained by adding 4 to ( x ). This creates a linear relationship between ( x ) and ( y ). For example, when ( x = 0 ), ( y = 0 + 4 = 4 ), and when ( x = 1 ), ( y = 1 + 4 = 5 ). These ordered pairs ( x, ) form a table of values that can be plotted on a graph to visualize the linear relationship between the variables.

Let's consider a few values to illustrate:

`\[ \begin{align*} (x, y) & : (0, 4), (1, 5), (2, 6), (3, 7), \ldots \end{align*} \]`\[ \begin{align*}

(x, y) & : (0, 4), (1, 5), (2, 6), (3, 7), \ldots

\end{align*} \]

In each case, the ( y )-value is consistently 4 more than the ( x )-value. This pattern continues indefinitely. Therefore, any table of values where ( y ) is equal to ( x ) plus 4 can be represented by the function ( y = x + 4 ).

Understanding the function in this way provides a clear method for generating a table of values, graphing the function, and grasping the fundamental relationship between the input ( x ) and output ( y ) in a linear context. This type of linear function is commonly encountered in various mathematical and real-world scenarios.

Answer 2

See explanation

Step-by-step explanation:

The given function is
`y=x+4`

To create a table we choose some values of x and plug it into the function and solve for y.

When x=-1,
`y=-1+4=3`

When x=0 y=0+4

When x=1, y=4+1=5

When x=2, y=6

The table looks like;

x y

-1 3

0 4

1 5

2 6