Question

The table below shows the value for the function y=f(x)If g(x)=1/2 which of the following are solutions to g(x) select all that applyA (-3,5.5)B(-1,-2)C(0,4)D (5,-8)

Answer 1

So we have a table of values that associate x values with a function f(x). The pairs (x,y) are solutions to the equation y=f(x) and they are:

`\begin{gathered} (-3,5) \\ (-1,-4) \\ (0,2) \\ (5,-8) \\ (6,3) \end{gathered}`

If we define a new function g(x)=(1/2)*f(x) its solutions will be those of f(x) but with their y values divided by 2. Then the solutions to g(x) are:

`\begin{gathered} (-3,(5)/(2))=(-3,2.5) \\ (-1,-(4)/(2))=(-1,-2) \\ (0,(2)/(2))=(0,1) \\ (5,-(8)/(2))=(5,-4) \\ (6,(3)/(2))=(6,1.5) \end{gathered}`

Then the only option with a solution to g(x) is the second option (-1,-2).