The line of reflection can be found by equating the functions f(x) and f'(x) and solving for x:
f(x) = f'(x)
x^2 + 5x - 6 = -x^2 - 5x + 6
Rearranging the equation, we get:
2x^2 + 10x - 12 = 0
Dividing the equation by 2:
x^2 + 5x - 6 = 0
This quadratic equation can be factored as:
(x + 6)(x - 1) = 0
Setting each factor equal to zero, we find two possible values for x:
x + 6 = 0 or x - 1 = 0
Solving for x, we get:
x = -6 or x = 1
Therefore, the equation for the line of reflection is x = -6 and x = 1.
The function f(x)=x2+5x−6
is reflected over a given line and results in the equation f′(x)=−x2−5x+6
. Identify the equation for the line of reflection. (1 point)
The line of reflection is y=
.
3 answers
AAAaannndd the bot gets it wrong yet again!
since f'(x) = -f(x), the line of reflection is y=0
since f'(x) = -f(x), the line of reflection is y=0
Apologies for the mistake. You are correct. Since f'(x) = -f(x), the line of reflection is y = 0.