Which of the following equations correctly describes the function in the table using function notation? x y 0 -2 2 4 4 10 6 16 (1 point) Responses f(x)=x−2 f of x is equal to x minus 2 f(x)=2x f of x is equal to 2 x f(x)=3x−2 f of x is equal to 3 x minus 2 f(x)=2x+4

Answer 1

To determine which equation correctly describes the function in the table, we need to analyze the given pairs of $(x,y)$:

• When $x=0$, $y=-2$
• When $x=2$, $y=4$
• When $x=4$, $y=10$
• When $x=6$, $y=16$

We'll test each proposed function to confirm which one fits the values in the table.

1. For $f(x)=x-2$:

   • $f(0)=0-2=-2$ (correct)
   • $f(2)=2-2=0$ (incorrect, should be 4)
   • This function does not match.

2. For $f(x)=2x$:

   • $f(0)=2(0)=0$ (incorrect, should be -2)
   • This function does not match.

3. For $f(x)=3x-2$:

   • $f(0)=3(0)-2=-2$ (correct)
   • $f(2)=3(2)-2=6-2=4$ (correct)
   • $f(4)=3(4)-2=12-2=10$ (correct)
   • $f(6)=3(6)-2=18-2=16$ (correct)
   • This function matches all points.

4. For $f(x)=2x+4$:

   • $f(0)=2(0)+4=4$ (incorrect, should be -2)
   • This function does not match.

The correct function that describes the relationship in the table is:

$f(x)=3x-2$