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

Question

.

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

(2 points)
x 0 1 2
−f(−x)
Remaining Attempts : 3

Answer 1

To analyze the reflection of the function $f(x)=(x+2{)}^2+1$, we first need to create a table of values for $f(x)$ evaluated at $x=0$, $x=-1$, and $x=-2$.

Step 1: Calculate $f(x)$ at the specified points

1. When $x=0$: $$f(0)=(0+2{)}^2+1=2^2+1=4+1=5$$

2. When $x=-1$: $$f(-1)=(-1+2{)}^2+1=1^2+1=1+1=2$$

3. When $x=-2$: $$f(-2)=(-2+2{)}^2+1=0^2+1=0+1=1$$

Step 2: Create the table for $-f(-x)$

To find the values of $-f(-x)$, we will evaluate the function $f(x)$ at the corresponding negative values of $x$:

• For $x=0$, $-f(-0)=-f(0)=-5$
• For $x=1$, $-f(-1)=-f(-1)=-2$
• For $x=2$, $-f(-2)=-f(-2)=-1$

Final Table

Here’s the completed table with values for $f(x)$ and $-f(-x)$:

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

This shows the values of $f(x)$ at the specified points and the corresponding values of $-f(-x)$, which can illustrate the reflection property of the function.