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kotegsom [21]
2 years ago
5

Give an equation for the result of shifting the graph of up by 4 units, and left by 2 units.

Mathematics
1 answer:
andreyandreev [35.5K]2 years ago
3 0

We define transformations as operators that act on functions by modifying them in some given way. One type of transformation is a translation, which will move the whole graph of the function in some give direction.

For a general function f(x), we will find that the equation for the result of shifting the graph up by 4 units and left by 2 units is:

g(x) = f(x + 2) + 4

----------------------------------

Let's see how to solve this.

We need to start by defining the two most common translations (also known as shifts).

Horizontal translation:

For a given function f(x), an horizontal translation of N units is written as:

g(x) = f(x + N)

where if N is positive,<em> the translation is to the left.</em>

If N is negative, <em>the translation is to the right.</em>

Vertical translation:

For a given function f(x), a vertical translation of N units is written as:

g(x) = f(x) +  N

Where if N is positive,<em> the translation is upwards.</em>

If N is negative, <em>the translation is downwards.</em>

Here for an unknown function f(x), we want to write the equation that gives a shift up of 4 units and left by 2 units.

<em>The shift up of 4 units is written as:</em>

<em>g(x) = f(x) + 4</em>

<em>The shift of 2 units to the left is written as:</em>

<em>g(x) = f(x + 2) </em>

<em>These two together give:</em>

<em>g(x) =  f(x + 2) + 4.</em>

This is the equation we wanted to get.

If you want to learn more, you can read:

brainly.com/question/24401156

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P(x)=2x^3-11x^2+ax-40 if x+4 is a factor of this polynomial what is the value of a
Vika [28.1K]

Answer:

a = -86.

Step-by-step explanation:

By the Factor Theorem, if x + 4 is a factor then P(-4) = 0, so:

P(-4) = 2(-4)^3 - 11(-4)^2 + a(-4)- 40 = 0

-128 - 176 - 4a - 40 = 0

-4a = 128 +176 + 40

-4a = 344

a = -86.

3 0
3 years ago
A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled
n200080 [17]

Answer:

24000 pieces.      

Step-by-step explanation:

Given:

Side lengths of cube = \frac{1}{4} \ foot

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

Volume\ of\ cube =a^{3}

                          =\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot

                                   

Length = 8 foot, Breadth = 6\frac{1}{4} =\frac{25}{4} \ foot, Height =7\frac{1}{2} =\frac{15}{2} \ foot

Volume\ of\ rectangular\ prism =length\times breadth\times height

                                                =8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = \frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.                                

7 0
3 years ago
Help,anyone can help me do quetion,I will mark brainlest.​
Serhud [2]

Answer:

a)    x = 2

b)    x = 4

Step-by-step explanation:

a = (b₁ + b₂)/2 * h

----------------------------

a)

48 = (10 + x)/2 * 8

Divide both sides by 8

6 = (10 + x)/2

multiply both sides by 2

12 = 10 + x

Subtract 10 from both sides

2 = x

x = 2

---------------------------------

b)

18 = (7 + 2)/2 * x

18 = 4.5 * x

divide both sides by 4.5

4 = x

x = 4

5 0
3 years ago
Read 2 more answers
Please help as I'm confused / very tired so I can't think right now...
Masteriza [31]
Median is the middle number so it would be 250

8 0
3 years ago
Read 2 more answers
In hours Mariah can rake 3 backyards. how much of a backyard can she rake in 1hour?​
Leviafan [203]

Answer: 3 or the whole backyard

Step-by-step explanation: In a hour she can rack 3 backyard. The question asked that how much of a backyard can she rake in 1 hour. She can rake the whole backyard in a hour.

7 0
3 years ago
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