Below are the graphs \( f(x) = |x| \) and its transformation \( g(x) \).What is the equation for \( g(x) \)?### Graph ExplanationThe first graph displays the absolute value function \( f(x) = |x| \), which is a V-shaped graph symmetric with respect to the y-axis. The vertex of the graph is at the origin (0,0), and it opens upwards.The second graph shows a transformed version of the absolute value function. It appears to be flipped vertically and shifted horizontally to the left and possibly shifted vertically.### Multiple Choice Options- \( g(x) = |x + 3| + 2 \)- \( g(x) = |-x + 3| + 2 \)- \( g(x) = -|x| + 2 \)- \( g(x) = -|x + 3| + 2 \)The task is to identify the correct equation for \( g(x) \) based on the transformation of the original graph \( f(x) = |x| \).

Answered: Image /qna-images/answer/06b1e8f8-ed53-42c5-a14e-ead1a17c48ff.jpg

Below are the graphs f(x) = |x|and its transformation g (x). What is the equation for g(x). -5 -4 -3 -1 3 -4 -4 -5 f(x) = |x| g(x) = ? O g (a) = |æ + 3| + 2 O g (x) = |- æ + 3| + 2 O g(x) = -læl + 2

Below are the graphs f(x) = |x|and its transformation g (x). What is the equation for g(x). -5 -4 -3 -1 3 -4 -4 -5 f(x) = |x| g(x) = ? O g (a) = |æ + 3| + 2 O g (x) = |- æ + 3| + 2 O g(x) = -læl + 2

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: f(x) -6-5-4-3-2 6 5 4 3 2 -5 -6 1 2 3 4 5 6 g(x)

A: A graph of the functions and are given.The aim is to find the intercept of these functions.

Q: graph g(x)= 2(x+3)2 - 1 using transformations

Q: If f(x) = x2 is translated 3 units to the right to form g(x), which of the following equations best…

Q: Sketch the graph of g if (3x + 4)(x – 1) g(x) (2x – 5)(x – 1)

A: Given, gx=3x+4x-12x-5x-1

Q: Ketch a graph of f(x) = 3 2 x + 2

Q: The graph shows the functions f(x) = |2x— 2| and g(x) = |2x +2|. If g(x) is written in the form f (x…

A: Given that; f(x)= |2x-2|g(x)= |2x+2| From the statement; g(x) = f(x+k) ... (i) Value of k = ?

Q: D. Describe how to obtain the graph of g and h if g(x) = 2(x + 2)² – 3, h(x) = 2x² , and h(x) = 2(x…

A: Given: Let g(x)=2x+22-3 and h(x)=2x-32+2 from the function fx=2x2. Properties of the transformation…

Q: The graph of f(x) = x³ is reflected over the y-axis, vertically stretched by by a fac- tor of 4,…

A: The original function is f(x) Thenf(-x) reflects the graph about y-axis.k f(x) stretches the graph…

Q: Sketch a graph of f(x) = = -5 -4 -3 -2 -1 Clear All Draw: 4 3 2+ H -1 -2 -3 -4 3 N|W 2+1 2 3 10 .

Q: g(x + h) – g(x) g(x) = -x² – x + 9 Given the function find the difference quotient h

Q: Use the graphs of f and g to find (fg)(-1). f(x)• Ay Q 6 4 2 -6 -4 -2 2 g(x) 4 6 f(x) g(x) X

A: Step 1: The expression (fg)(−1) is the operation of multiplying their individual functions at that…

Q: The graph of f(x)=x is shifted left 5 units to arrive at the graph of g(x). What is the rule for…

Q: If f(x) has a domain x≤-1 and range y≥-1 , then determine the domain and range of g(x) given that…

Q: Let f(x) = 4x + 5 and g(x) = 5x² + 2x. After simplifying, (fog)(x) = =

Q: Find an equation for the graph sketched below f(x) = 8+ 74 -5-4-3 -2 -I 65 5₂ I 3 2 1 my na mg -1 -3…

A: Using a base function and graph, we can solve the question.

Q: If the point (3, 11) is on the graph of f(x), what point is on the graph of g(x) = - 2f(x+3)? О (0,…

A: The point 3,11 is on the graph of the function fx. To evaluate : What point is on the graph of the…

Q: How is the graph of g(x) = (x - 5)2 - 5 related to the graph of f(x)=x²2? The graph of g(x) = (x -…

A: I am attaching image so that you understand each and every step.

Q: Given the function f(x) = (x - 1)(x + 3) (x - 2) Explain & determine how we could find the…

A: Given that Reploace x by 3x in f(x) then Multiply both sides with -2…

Question

Below are the graphs \( f(x) = |x| \) and its transformation \( g(x) \).

What is the equation for \( g(x) \)?

### Graph Explanation

The first graph displays the absolute value function \( f(x) = |x| \), which is a V-shaped graph symmetric with respect to the y-axis. The vertex of the graph is at the origin (0,0), and it opens upwards.

The second graph shows a transformed version of the absolute value function. It appears to be flipped vertically and shifted horizontally to the left and possibly shifted vertically.

### Multiple Choice Options

- \( g(x) = |x + 3| + 2 \)
- \( g(x) = |-x + 3| + 2 \)
- \( g(x) = -|x| + 2 \)
- \( g(x) = -|x + 3| + 2 \)

The task is to identify the correct equation for \( g(x) \) based on the transformation of the original graph \( f(x) = |x| \).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The graph of the function is a translation of the graph of f(x) = x³. Graph the function. h(x) : (x + 4)3 + 1 y y 6- 4 4 2 2 X -6 -4 -2 -6 -4 -2 2 4 6 -2 -2 -4 -6F -6F y y 6- 6- 4 4 2 2 X -6 -4 -2 2 4 -6 -4 -2 2 4 6 -2 -2 -4 -4 -6F -6F
1 -x + 2. No work needs to be shown for this problem. 2 Sketch a graph of f(x) -2 -1 3 -1 -2 -3 -4
The function f (x) undergoes a vertical compression by a factor of, a horizontal shift left 4 units, and a vertical shift down 2 units to become g(x). Which equation describes g (x)? ○ g(x) = 3x + 4| – 2 ○ g(x) = |x g(x) = ○ g(x) = T 4+2 |x 4| 2 x + 4 + 2
Use the graphs of f and g to find (fg)(1). -6 -4 6 4 -2 2 4 f(x) (X) 6 X Q G (fg)(1)=