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
evablogger [386]
3 years ago
6

The question is in the screenshot attached. Thank you!

Mathematics
1 answer:
Rzqust [24]3 years ago
7 0

Answer:

Domain: -4 < x < 4

Zeros: (-2, 0), (0, 0) and (2, 0)

The function is positive if: 0 < x < 2

The function is negative if: -4 < x < 0 and 2 < x < 4

Step-by-step explanation:

Domain of the function are those x values where the function is defined, For this case, -4 < x < 4

Zeros of a function are those x values where y = 0, that is, the graph intersect x-axis. For this case, the points are: (-2, 0), (0, 0) and (2, 0)

The function is positive if the graph o the function is above x-axis. For this case, the function is positive at the interval (0, 2)

The function is negative if the graph o the function is below x-axis. For this case, the function is negative at the intervals (-4, 0) and (2, 4)

You might be interested in
The tangent to the circle x^2+y^2=18 is parallel to the tangent x+y=6
liubo4ka [24]

Answer:

y = -x - 6

Step-by-step explanation:

If we are looking for the equation of the line tangent to the circle, we have to find the first derivative of the circle function.  If that tangent line is to be parallel to the given tangent line, we need to find the slope of the the given tangent line and make sure the slope of the line we are looking for is the same.  First let's find the slope of the given tangent.  If the given tangent is x+y=6, then to find the slope, solve for y:

y = -x + 6.  So the slope of that line, and also the slope of the tangent we are solving for, is -1.  Hold that thought while we find the derivative of the function.  Using implicit differentiation, we find the derivative to be:

2x+2y\frac{dy}{dx}=0

Solving for the slope (dy/dx) gives us:

2y\frac{dy}{dx}=-2x and

\frac{dy}{dx}=\frac{-2x}{2y} so

\frac{dy}{dx}=-\frac{x}{y}

Subbing in the value of the slope we found:

-1=-\frac{x}{y} so

-y = -x or, equivalently,

y = x.  Now that we know that y and x are the same value, we can go back to the original circle to find out what they both are by substitution.  If y = x, we make the substution:

If x^2+y^2=18, then

y^2+y^2=18 and

2y^2=18 and

y^2=9 so

y = ±3

We will choose the negative root (you'll see why in a second) and sub that in for both y and x since y and x are th same number.  Going back to the fact that the slope is -1:

y - (-3) = -1(x - (-3)) simplifies a bit to:

y + 3 = -x - 3 which gives us, in slope-intercept form:

y = -x - 6

That is the equation of the tangent to the circle that is parallel to the given tangent.

If we would have chosen the principle (or positive) root of 3, our equation would have looked like this:

y - 3 = -1(x - 3) and

y = -x + 3 + 3 so

y = -x + 6.  Notice that that is the EXACT SAME EQUATION as the given tangent.  That's why we have to pick the negative 3 as our root.

Good luck in your calculus class!  Make sure you post your questions in here!  Many of us LOVE the challenge of calculus!

3 0
3 years ago
What is the volume of the sphere
Firdavs [7]

Answer:

Formula for Volume=4/3 π r^3

Step-by-step explanation:

3 0
3 years ago
How do these functions differ from functions you have used in algebra in the past?
ICE Princess25 [194]

Answer:s

Step-by-step explanation:

5 0
3 years ago
Need help now please
Umnica [9.8K]

Answer:

f(13)=105

f(4)=58

f(6)=-5

f(7)=26

Step-by-step explanation:

Good luck

6 0
3 years ago
How many solutions does this system have?<br> -x + 2y = 16 <br>4x - 8y = -64​
Doss [256]
Infinite number of solutions
Multiply first equation by -4
You would get the same equation as the second one
6 0
3 years ago
Other questions:
  • Bro help me figure this out please
    6·1 answer
  • The graph shows a proportional relationship between the number of kilometers traveled by a bicycle (y) and the number of minutes
    8·2 answers
  • List the LCM of the numbers. (MCC.6.NS.4)<br> 3, 11, 12
    11·1 answer
  • What is 10/2 equal to 1/5
    10·1 answer
  • Jimmy ran with a speed of m miles per hour. How far did he run in t minutes?
    6·1 answer
  • Which transformation of triangle T will produce triangle U?
    11·1 answer
  • Solve.<br> Five times a number is 110 less than 7 times the number. Find the number.
    5·1 answer
  • Solve for x: please help
    8·2 answers
  • I need answer?????????????????????
    10·1 answer
  • 19. Since April 1, 1986 was a Tuesday, March,
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!