Question

2-31. does the table below appear to represent a function? if so, write an equation using function notation that represents the table. if not, explain why it cannot represent a function.
| figure #
x | 0 | 1 | 2 | 3 | 4 |
| # of tiles
y | 4 | 8 | 12 | 16 | 20 |

Explanation:

Step1: Check function definition

A function has one - to - one or many - to - one mapping. For each $x$ value in the table, there is exactly one $y$ value. So, it is a function.

Step2: Find the slope

The slope $m$ of a linear function is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(1,8)$. Then $m=\frac{8 - 4}{1 - 0}=4$.

Step3: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the table, when $x = 0$, $y=4$, so $b = 4$.

Step4: Write the function

The equation of a line in slope - intercept form is $y=mx + b$. Substituting $m = 4$ and $b = 4$, we get $y = 4x+4$. In function notation, $f(x)=4x + 4$.

Answer:

Yes, it is a function. The function notation is $f(x)=4x + 4$.