Question

A, B, C, or D please?

I just don’t understand this

Answer 1

`f(x)=\frac25x+\frac35`

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:
`f(x)=\frac25x+\frac35`