Question

The table represents the function . Fill in the blanks based on the information given in the table. x f(x) -4 -66 -3 -29 -2 -10 -1 -3 0 -2 1 -1 2 6   (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Is this a linear or nonlinear function? Response area When , Response area. When , Response area. -3-29-10-10cannot be determined based on the tablenonlinear6-66

Answer 1

To determine if the function is linear or nonlinear, we can look at the differences in the function values \( f(x) \).

1. Calculate the change in \( f(x) \) as \( x \) changes:

   • From \( x = -4 \) to \( x = -3 \):

     • \( f(-4) = -66 \) and \( f(-3) = -29 \)
     • Change = \( -29 - (-66) = 37 \)

   • From \( x = -3 \) to \( x = -2 \):

     • \( f(-3) = -29 \) and \( f(-2) = -10 \)
     • Change = \( -10 - (-29) = 19 \)

   • From \( x = -2 \) to \( x = -1 \):

     • \( f(-2) = -10 \) and \( f(-1) = -3 \)
     • Change = \( -3 - (-10) = 7 \)

   • From \( x = -1 \) to \( x = 0 \):

     • \( f(-1) = -3 \) and \( f(0) = -2 \)
     • Change = \( -2 - (-3) = 1 \)

   • From \( x = 0 \) to \( x = 1 \):

     • \( f(0) = -2 \) and \( f(1) = -1 \)
     • Change = \( -1 - (-2) = 1 \)

   • From \( x = 1 \) to \( x = 2 \):

     • \( f(1) = -1 \) and \( f(2) = 6 \)
     • Change = \( 6 - (-1) = 7 \)

2. The changes in \( f(x) \) are not consistent:

   • 37, 19, 7, 1, 1, and 7.

Since the changes in the \( f(x) \) values do not remain constant, the function is nonlinear.

Now, based on the responses to fill in the blanks:

• Is this a linear or nonlinear function? nonlinear
• When \( x = -3 \), \( f(x) = -29 \)
• When \( x = -2 \), \( f(x) = -10 \)

So the filled-in responses would be:

1. nonlinear
2. -3, -29
3. -2, -10