The function f(x)=2(x+22) is shown in the graph. Which table shows that g(x)=−f(−x) results in a reflection about the origin of the function graphed? Hint: Make a table of the x - and y -coordinates based on the graph. Use these points to determine the coordinates of the function reflected about the origin. (1 point) Responses
x g(x) 1 −2 2 0 3 −2
x g(x) 1 2 2 0 3 2
x g(x) −1 −2 −2 0 −3 −2
x g(x) −1 2 −2 0 −3 2
The correct table that shows the reflection about the origin of the function graphed is:
x g(x)
1 -2
2 0
3 -2
Explanation: To find g(x), we need to substitute -x into the function f(x)=2(x+22) and negate the entire expression.
For x = 1, -x = -1, so g(1) = -f(-1) = -2(1+22) = -2(23) = -46.
For x = 2, -x = -2, so g(2) = -f(-2) = -2(2+22) = -2(24) = -48.
For x = 3, -x = -3, so g(3) = -f(-3) = -2(3+22) = -2(25) = -50.
Therefore, the table x g(x) -1 -2 -2 0 -3 -2 represents the reflection about the origin of the function graphed.