Answer:
[tex]f(x)=\dfrac25x+\dfrac35[/tex]
Step-by-step explanation:
The data in the table means that if you input the value of x into the function, the output will be f(x).
The first two answer options are linear functions. If a function is linear, the ratio of the difference in y-values to the difference in x-values is always constant.
We can see that the x-values in the table increase by 3 each time, so the difference in x-values is 3.
By calculation, we can also see that the y-values increase by 6/5 each time, so the difference in y-values is 6/5.
Therefore, the ratio of differences is 6/5 ÷ 3 = 2/5 and is constant.
So the function is linear and has a slope (gradient) of 2/5
Therefore, the function is: [tex]f(x)=\dfrac25x+\dfrac35[/tex]
