Question

15. Which function represents the data in the table?X64106158.5f(x)2.5C.a. f(x) = 2x + 1b. f(x) = -1d.16. The function f(x) = x - 9 is shifted 2 units up and 3 units to the left. Sea. f(x) = 2x - 6b. f(x) = (x – 3) +7d. 1

Answer 1

From the table given

We can see that

when x=3, f(x)=2.5

when x=6, f(x) =4

when x=10, f(x)=6

when x=15, f(x)=8.5

If two coordinates are selected, then we can find the relationship by using the equation below

`(y_2-y_1)/(x_2-x_1)=\frac{y_{}-y_1}{x_{}-x_1}`

If we select the points

x=6 and f(x)=4

x=10 and f(x)=6

Therefore, If we substitute these values

`\begin{gathered} (6-4)/(10-6)=(y-4)/(x-6) \\ \\ (2)/(4)=(y-4)/(x-6) \\ \\ (1)/(2)=(y-4)/(x-6) \\ \end{gathered}`

`\begin{gathered} \text{cross multiply} \\ y-4=(1)/(2)(x-6) \\ \\ y-4=(1)/(2)x-3 \\ \\ y=(1)/(2)x-3+4 \\ \\ y=(1)/(2)x+1 \end{gathered}`

Answer=>

y=1/2x+1