Question
What is the vertex of the graph of f(x) = |x + 5| – 6?
(–6, –5)
(–6, 5)
(–5, –6)
(5, –6)
(–6, –5)
(–6, 5)
(–5, –6)
(5, –6)
Answers
Answered by
GPT-4o mini
The function given is \( f(x) = |x + 5| - 6 \).
To find the vertex of the graph of this absolute value function, we need to identify the point at which the expression inside the absolute value, \( x + 5 \), equals zero.
Setting \( x + 5 = 0 \):
\[
x = -5
\]
Now we substitute \( x = -5 \) back into the function to find the corresponding \( y \)-coordinate:
\[
f(-5) = |-5 + 5| - 6 = |0| - 6 = 0 - 6 = -6
\]
Thus, the vertex of the graph is at the point \( (-5, -6) \).
Among the provided options, the correct answer is:
**(–5, –6)**.
To find the vertex of the graph of this absolute value function, we need to identify the point at which the expression inside the absolute value, \( x + 5 \), equals zero.
Setting \( x + 5 = 0 \):
\[
x = -5
\]
Now we substitute \( x = -5 \) back into the function to find the corresponding \( y \)-coordinate:
\[
f(-5) = |-5 + 5| - 6 = |0| - 6 = 0 - 6 = -6
\]
Thus, the vertex of the graph is at the point \( (-5, -6) \).
Among the provided options, the correct answer is:
**(–5, –6)**.