Question

Find the linear function f(x) for which both f(−2) = 6 and f(0) = −4. Which one of the following matches the correct function?a. f(x) = -1/5xb. f(x) = 6x-4 c. f(x) = -1/5x-4d. -5x-4

Answer 1

SOLUTION:

Given:

f(x)= ?

f(-2) = 6

f(0) = -4

We will answer this question by testing the options with our given values

$\begin{gathered} A)\text{ f(x)=}\frac{-1}{5x} \\ f(-2)=\text{ }\frac{-1}{5(-2)} \\ f(-2)=\text{ }\frac{-1}{-10} \\ f(-2)=\text{ }\frac{1}{10} \\ \text{Does not equate with f(-2)=6} \end{gathered}$$\begin{gathered} B)\text{ f(x)= 6x-4} \\ f(-2)\text{ = 6(-2)-4} \\ f(-2)=-12-4 \\ f(-2)=-16 \\ \text{Does not equate with f(-2)=6} \end{gathered}$$\begin{gathered} C)\text{ f(x)=}\frac{-1}{5x-4} \\ f(-2)=\text{ }\frac{-1}{5(-2)-4} \\ f(-2)=\text{ }\frac{-1}{-10-4} \\ f(-2)=\text{ }\frac{-1}{-14} \\ f(-2)=\text{ }\frac{1}{14} \\ \text{Does not equate with f(-2)=6} \end{gathered}$$\begin{gathered} f(x)=-5x-4 \\ f(-2)\text{ = -5(-2)-4} \\ f(-2)\text{ = 10-4} \\ f(-2)\text{ = }6. \\ \text{Checks well with original statement} \\ On\text{ the other hand} \\ f(0)\text{ = -5(0) -4} \\ f(0)\text{ = 0-4} \\ f(0)\text{ = -4} \\ \text{Fits well with original statement} \end{gathered}$

Final answer. The right function is f(x)= -5x-4. Option D