1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
creativ13 [48]
3 years ago
7

Algebraically determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, the origin or has no symmet

ry.
Mathematics
1 answer:
Gala2k [10]3 years ago
7 0
\bf y=x^3-4x
\\\\\\
\textit{check for y-axis symmetry}\\\\
\stackrel{x=-x}{y=(-x)^3-4(-x)}\implies y=(-x)(-x)(-x)+4x\implies \boxed{y=-x^3+4x}
\\\\\\
\textit{checking for x-axis symmetry}\\\\
\stackrel{y=-y}{(-y)=x^3-4x}\implies -y=x^3-4x\implies \boxed{y=-x^3+4x}
\\\\\\
\textit{checking for origin symmetry}\\\\
\stackrel{x=-x\qquad y=-y}{(-y)=(-x)^3-4(-x)}\implies -y=(-x)(-x)(-x)+4x
\\\\\\
-y=-x^3+4x\implies y=\cfrac{-x^3+4x}{-1}\implies \boxed{y=x^3-4x}\quad \checkmark

notice, if you replace x = -x and y = -y accordingly for each test for symmetry, if the resulting function, is equal to the original function, then it has that type of symmetry.
You might be interested in
Which of the following equations could be used to determine the value of X
Tcecarenko [31]

Answer:

D

Step-by-step explanation:

If the original price is x and you deduct 3, you'l have x - 3.

If you buy 4 of them, you multiply that price by 4, giving you 4(x - 3).

Then, if that value is equal to 27, you get 4(x - 3) = 27

5 0
3 years ago
Read 2 more answers
A=5 and c=13 what is the value of b?​
Anarel [89]

Answer: 8 is the answer

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Help ASAP <br><br> 30 + x = 2035
max2010maxim [7]

Answer: 2005

Step-by-step explanation:

2035-30=x

8 0
3 years ago
Read 2 more answers
If f(x) = 5x + 1 and g(x) = 2x - 4 find f(x) + g(x)
Naddika [18.5K]

Answer:

f(x)+g(x)= 7x-3

Step-by-step explanation:

(5x+1)+(2x-4)

lets put each like term together

(5x+2x)(1-4)

add:

7x-3

4 0
3 years ago
ms. rivera has 4,386 pencils. if 2,498 are already broken how many pencils does ms. rivera still have to write with?
Artemon [7]

Answer:

1,888 pencils

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • I really need help with this problem
    9·1 answer
  • What expression is equivalent to (fg) (5)
    13·2 answers
  • What is the answer to 6a + 11 if a =8
    14·2 answers
  • Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the gi
    12·2 answers
  • What is true about the dilation?
    13·1 answer
  • Given that the measure of &lt;1 is 40⁰, what is the measure of &lt;BUR?​​
    15·1 answer
  • Please help me answer <br> 42<br> 10<br> 7<br> 9
    12·1 answer
  • What is the approximate length of minor arc XZ? Round to the nearest tenth of a meter. 1.8 meters 3.7 meters 15.2 meters 18.8 me
    8·2 answers
  • Find the median of the data in the dot plot below.
    10·1 answer
  • Determine el área del siguiente rectángulo
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!