To determine whether the function represented by the table is linear or nonlinear, we can analyze the differences in the \( f(x) \) values as \( x \) increases.
-
Calculate the differences:
- For \( x = -4 \) to \( x = -3 \): \[ f(-3) - f(-4) = -29 - (-66) = 37 \]
- For \( x = -3 \) to \( x = -2 \): \[ f(-2) - f(-3) = -10 - (-29) = 19 \]
- For \( x = -2 \) to \( x = -1 \): \[ f(-1) - f(-2) = -3 - (-10) = 7 \]
- For \( x = -1 \) to \( x = 0 \): \[ f(0) - f(-1) = -2 - (-3) = 1 \]
- For \( x = 0 \) to \( x = 1 \): \[ f(1) - f(0) = -1 - (-2) = 1 \]
- For \( x = 1 \) to \( x = 2 \): \[ f(2) - f(1) = 6 - (-1) = 7 \]
The differences of \( f(x) \) are not consistent; they are \( 37, 19, 7, 1, 1, 7 \). Since the differences are not constant, the function is nonlinear.
- Fill in the blanks:
- Is this a linear or nonlinear function? Nonlinear
- Complete the statements:
- When \( x = 0 \), \( f(0) = -2 \)
- When \( x = 2 \), \( f(2) = 6 \)
So the answers are:
- Is this a linear or nonlinear function? Nonlinear
- When \( x = 0 \), \( f(0) = -2 \)
- When \( x = 2 \), \( f(2) = 6 \)