Question

Create a table for the reflection about the origin of the function f(x)=(x+2)2+1
.

Hint: First create a table of values for f(x)
evaluated at x=0
, x=−1
., and x=−2
.

(2 points)
Determining the corresponding -f(-x) values to fill in the missing entries for the given x values.
x 0 1 2
−f(−x)

Answer 1

First compute f at the hinted x-values:
- f(0) = (0+2)^2 + 1 = 4 + 1 = 5
- f(-1) = (-1+2)^2 + 1 = 1 + 1 = 2
- f(-2) = (-2+2)^2 + 1 = 0 + 1 = 1

Now the reflection about the origin is y = -f(-x). For the requested x = 0,1,2:

- -f(-0) = -f(0) = -5
- -f(-1) = -f(-1) = -2
- -f(-2) = -f(-2) = -1

Table:

x | 0 | 1 | 2
--|---|---|---
−f(−x) | -5 | -2 | -1