**Graph of a Function and Its Symmetry**The graph of a function defined for $x \geq 0$ is given in the first diagram. ### Part (a)**Complete the graph for $x < 0$ to make an even function.**An even function satisfies the property $f(x) = f(-x)$. This means the graph must be symmetric with respect to the y-axis. Below the given function graph, you have four possible graphs that attempt to complete the given function for $x < 0$:1. **Left Side Graph 1:** - This graph correctly mirrors the original function on the given side over the y-axis.2. **Right Side Graph 1:** - This graph includes mirrored portions, but not all parts correctly overlay with the original function.3. **Left Side Graph 2:** - This graph, again, mirrors the original but doesn’t accurately reflect the peaks and troughs of the given function over the y-axis.4. **Right Side Graph 2:** - Similarly, this graph doesn’t accurately reflect the symmetry required for an even function.### Part (b)**Complete the graph for $x < 0$ to make an odd function.**An odd function satisfies the property $f(-x) = -f(x)$. This means the graph must be symmetric about the origin. Below are four additional possible ways the function can be extended to $x < 0$:1. **Left Side Graph 1:** - The graph correctly reflects the original function rotated 180 degrees about the origin.2. **Right Side Graph 1:** - This completion also shows an appropriate rotation indicating an odd function.3. **Left Side Graph 2:** - This graph reflects incorrect symmetry, which doesn’t satisfy the property of an odd function.4. **Right Side Graph 2:** - This graph shows an inaccurate rotation and doesn’t meet the requirements for an odd function. ### Detailed Explanation of Diagrams- **Given Graph:** Displays a function from $x = 0$ to $x > 0$.- **Even Function Completion Options:** - The correct diagrams provide a y-axis reflection of the given function ensuring symmetry.- **Odd Function Completion Options:** - The accurate diagrams show a 180-degree rotation ensuring the function satisfies the origin

There graph of an even function is symmetric about y axis.

Answered: The graph of a function defined for…

The graph of a function defined for x20is given. y (2) Complete the graph forx< 0 to make an even function. vinain (b) Complete the graph for x<0 to make an odd function. y

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: Evaluate f( - 3) where f(r) is the piecewise function graphed below. f(- 3) =

A: Value of the function under f

Q: Consider the graph of the piecewise function h (x) below 10 RED PIECEN 5- GREEN PIECE -10 0. 10…

A: Given: We have given the graph of function which is show below:

Q: For the piecewise function, find the values h(-5), h(-3), h(3), and h(6). -5x-16, for x<-4 h(x) = 3,…

Q: For f(x) = √10-2% @ Find the domain. Write answer in internal notation 6 Graph f(x) = √10-22.…

A: Domain: The set of values for which a function f(x) is defined is called the domain of the…

Q: 15. f(x) =

Q: Which could be the graph of f(x)=|x-h|+k if h and k are both positive?

Q: Use the graph to determine if the function is even, odd, or neither. 4) -3 -2 1 -1+ 1 2 3 x

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

**Graph of a Function and Its Symmetry**

The graph of a function defined for $x \geq 0$ is given in the first diagram.

### Part (a)
**Complete the graph for $x < 0$ to make an even function.**

An even function satisfies the property $f(x) = f(-x)$. This means the graph must be symmetric with respect to the y-axis. Below the given function graph, you have four possible graphs that attempt to complete the given function for $x < 0$:

1. **Left Side Graph 1:**
- This graph correctly mirrors the original function on the given side over the y-axis.

2. **Right Side Graph 1:**
- This graph includes mirrored portions, but not all parts correctly overlay with the original function.

3. **Left Side Graph 2:**
- This graph, again, mirrors the original but doesn’t accurately reflect the peaks and troughs of the given function over the y-axis.

4. **Right Side Graph 2:**
- Similarly, this graph doesn’t accurately reflect the symmetry required for an even function.

### Part (b)
**Complete the graph for $x < 0$ to make an odd function.**

An odd function satisfies the property $f(-x) = -f(x)$. This means the graph must be symmetric about the origin. Below are four additional possible ways the function can be extended to $x < 0$:

1. **Left Side Graph 1:**
- The graph correctly reflects the original function rotated 180 degrees about the origin.

2. **Right Side Graph 1:**
- This completion also shows an appropriate rotation indicating an odd function.

3. **Left Side Graph 2:**
- This graph reflects incorrect symmetry, which doesn’t satisfy the property of an odd function.

4. **Right Side Graph 2:**
- This graph shows an inaccurate rotation and doesn’t meet the requirements for an odd function.

### Detailed Explanation of Diagrams

- **Given Graph:** Displays a function from $x = 0$ to $x > 0$.
- **Even Function Completion Options:**
- The correct diagrams provide a y-axis reflection of the given function ensuring symmetry.
- **Odd Function Completion Options:**
- The accurate diagrams show a 180-degree rotation ensuring the function satisfies the origin

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Please show step by step work
if a 2 4- -5 -4 -3 -2 -1 2 3 5 4 -3 -4 -5 Clear All Draw: 1. Note: Be sure to include closed or open dots, but only at breaks in the graph. Get help: Video Video 2.
The function, y 00000000 -3x+6 is shown on the graph below. Use the graph to select all correct statements. == {x: -6 ≤ x ≤ 12} The x-intercept is: (9, 0) {x: xER} The x-intercept is: (0, 9) The y-intercept is: (0, 6) {y: YER} {y: -2 ≤ y ≤ 10} The y-intercept is: (6,0)
For the given graph, choose the statement below that is most accurate. O The graph could be a 3rd degree function because it has 3 zeros. O The graph could be a 4th degree function because it has 2 local extremes. The graph could be a 5th degree function because it has opposite end behavior. O The graph could be a 5th degree function because it has 3 inflection points and has opposite end behavior.
The function f is defined as follows. -3x+4 if x < 1 2x-1 if x21 (a) Find the domain of the function. (b) Locate any intercepts. f(x)= (c) Graph the function. (d) Based on the graph, find the range. (a) The domain of the function f is (Type your answer in interval notation.) (b) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) OB. There are no intercepts. (c) Choose the correct graph below. OA. -10 Q (d) The range of the function f is. (Type your answer in interval notation.) O B. 18 ... Q O C. O D. 1 Ау X Q Q
Please answer #12 using the graph. Show work and pick an answer from the multiple choice.
4