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Dmitry_Shevchenko [17]
3 years ago
5

How does the graph of g(x) = (x + 4)3 − 6 compare to the parent function f(x) = x3?

Mathematics
2 answers:
Semenov [28]3 years ago
8 0

Answer:

The parent function is f(x)=x^{3}

The transformed function is g(x)=(x+4)^{3} -6

In the transformed function, you can observe that there's being added four units to x-variable, and there's being subtracted six units from x-variable.

<em>These transformation means that the parent function is being moved 4 units leftwards and 6 units downwards, that's basically the relation between </em>f(x)<em> and </em>g(x)<em>.</em>

Now, you can get this answer by using the rules to translate functions:

  • If you add units to the x-variable, the graph will move to the left, if you subtract units to that variable, the graph will move to the right.
  • If you add units to y-variable, the graph will move upwards. If you subtract units from that variable, the graph will move downwards.

Solnce55 [7]3 years ago
4 0

Answer:

g(x) is shifted 6 units to the left

Step-by-step explanation:

Lets try to simplify g(x) since has a few extra terms:

g(x)= 3x+12-6=3x+6

Now it is easier to compare the two functions.

We can tell that they both have the same slope, both differs on a extra term

This term tell us that the g(x) is shifted to the left (it is positive 6)

Another approach to the solution is to plot the two functions together by obtaining the crossing points with the 'y' axis and with the 'x' axis

the result is shown in the attached picture

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What is the solution to this system of equations? 4x + 5y = 7
Nutka1998 [239]

Answer:

(-2, 3)

Step-by-step explanation:

4x + 5y = 7

3x - 2y = -12

Let's solve this by elimination. We want to eliminate one variable at a time. This means we need to multiply the equations to create a common multiple to cancel out a variable.

Let's work with y.

5y and -2y: For these values to cancel out, we need to multiply each term to create a common multiple.

2(4x + 5y = 7)

5(3x - 2y = -12)

Multiply.

8x + 10y = 14

15x - 10y = -60

Eliminate.

23x = -46

Divide both sides by 23.

x = -2

Now that we know x, let's plug it back into one of equations to find y.

4x + 5y = 7

4(-2) + 5y = 7

Multiply.

-8 + 5y = 7

Add.

5y = 15

Divide.

y = 3

Now we know x and y; let's plug both back into the equation we have not checked yet.

3x - 2y = -12

3(-2) - 2(3) = -12

Multiply.

-6 - 6 = -12

Subtract.

-12 = -12

Your solution is correct.

(-2, 3)

Hope this helps!

8 0
2 years ago
Jeremy will roll a number cube, numbered 1−6
Marina CMI [18]

Answer:

Step-by-step explanation:

p(even) = 3/6

p  number 3 = 1/6

p (even then number 3) = 3/6 * 1/6 = 3/36

7 0
3 years ago
What are the vertex, axis of symmetry, domain and range of the function:
DiKsa [7]
Y=(-x*x)-4x+3
y=-(x^2+4x-3)
4+y=-(x^2+4x+4)+3
y+4=-(x-2)^2.) +3
-4. -4
y=-((x-2)^2)-1

Answers:
Vertex: (2,-1)
AOS:x = 2
Domain: All Real Numbers
Range:[-1,Infinity)
3 0
3 years ago
What is the solution to the system of 4x-3y=1 and y+2x=3?
Svetradugi [14.3K]
By any chance will it be (1,1)
3 0
3 years ago
Read 2 more answers
How much it will take for a bag to travel 5 meters across the floor of it is traveling at 1 m/s
tester [92]
Time = \frac{distance}{speed}

The distance the bag will travel is 5 meters, and the speed it is traveling at is 1 m/s. Plug these into the formula for time.

\frac{5 m}{1 m/s} = 5 s
5/1 = 5 and the m (meters) cancel out, so you are left with s, seconds.

It will take the bag 5 seconds to travel across the floor.
5 0
3 years ago
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