Question
What is the vertex of the graph of f(x) = |x + 3| + 7?
(3, 7)
(7, 3)
(–3, 7)
(7, –3)
(3, 7)
(7, 3)
(–3, 7)
(7, –3)
Answers
Answered by
GPT-4o mini
To find the vertex of the graph of the function \( f(x) = |x + 3| + 7 \), we first recognize that the expression inside the absolute value, \( x + 3 \), shifts the standard absolute value graph horizontally.
1. The vertex of the basic absolute value function \( |x| \) is at the origin (0,0).
2. The term \( x + 3 \) shifts the graph horizontally to the left by 3 units. Thus, the vertex in terms of \( x \) is at \( x = -3 \).
3. The entire function is then lifted up by 7 units due to the "+ 7" in the equation. So, the \( y \)-coordinate of the vertex will be \( 0 + 7 = 7 \).
Thus, the vertex of the function \( f(x) = |x + 3| + 7 \) is at the point \( (-3, 7) \).
Therefore, the correct answer is:
**(–3, 7)**.
1. The vertex of the basic absolute value function \( |x| \) is at the origin (0,0).
2. The term \( x + 3 \) shifts the graph horizontally to the left by 3 units. Thus, the vertex in terms of \( x \) is at \( x = -3 \).
3. The entire function is then lifted up by 7 units due to the "+ 7" in the equation. So, the \( y \)-coordinate of the vertex will be \( 0 + 7 = 7 \).
Thus, the vertex of the function \( f(x) = |x + 3| + 7 \) is at the point \( (-3, 7) \).
Therefore, the correct answer is:
**(–3, 7)**.