Answered

From simple questions to complex issues, IDNLearn.com has the answers you need. Join our Q&A platform to access reliable and detailed answers from experts in various fields.

Select the correct answer.

What is the vertex of the function [tex]f(x)=|x-9|+2[/tex]?

A. [tex](9,2)[/tex]

B. [tex](-9,-2)[/tex]

C. [tex](-9,2)[/tex]

D. [tex](9,-2)[/tex]

Sagot :

GinnyAnsweridn
To find the vertex of the function [tex]\( f(x) = |x - 9| + 2 \)[/tex], let’s break it down step by step.

1. Understand the structure of the function:
- The given function is [tex]\( f(x) = |x - 9| + 2 \)[/tex].
- This is an absolute value function in the form [tex]\( f(x) = |x - h| + k \)[/tex], where [tex]\( h \)[/tex] and [tex]\( k \)[/tex] represent the horizontal and vertical shifts, respectively.

2. Identify the values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex]:
- The expression inside the absolute value is [tex]\( x - 9 \)[/tex].
- The value of [tex]\( x \)[/tex] that makes the expression [tex]\( x - 9 \)[/tex] equal to zero is [tex]\( x = 9 \)[/tex]. Therefore, [tex]\( h = 9 \)[/tex].
- The constant term added outside the absolute value is [tex]\( +2 \)[/tex]. So, [tex]\( k = 2 \)[/tex].

3. Determine the vertex of the function:
- In an absolute value function [tex]\( f(x) = |x - h| + k \)[/tex], the vertex of the graph is at the point [tex]\( (h, k) \)[/tex].
- Substituting our values of [tex]\( h \)[/tex] and [tex]\( k \)[/tex], we get the vertex at [tex]\( (9, 2) \)[/tex].

Therefore, the correct answer is:
A. [tex]\((9, 2)\)[/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.