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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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Find each Of change. Round to the nearest whole percent if necessary. State whether the percent Of change is an increase or 1. O
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Answer:

1. The percentage change is 74% and it is a percentage decrease

2. The percentage change is 15% and it is a percentage decrease

3. The percentage change is 20% and it is a percentage decrease

4. The percentage change is 43% and it is a percentage increase

5. The percentage change is 40% and it is a percentage decrease

6. The percentage change is 39% and it is a percentage decrease

Step-by-step explanation:

Given

1.\ Original = 5; New = 1.3

2.\ Original = 160; New = 136

3.\ Original = 15; New = 12

4.\ Original = 7; New = 10

5.\ Original = $30; New = $18

6.\ Original = 9.6; New = 5.9

Required

Determine the percentage change and state whether it's an increase or decrease

Percentage change is calculated as:

\%Change = \frac{New - Original}{Original} * 100\%

1.\ Original = 5; New = 1.3

\%Change = \frac{1.3 - 5}{1.3} * 100\%

\%Change = \frac{-3.7}5} * 100\%

\%Change = \frac{-3.7 * 100\%}{5}

\%Change = \frac{-370\%}{5}

\%Change = -74\%

<em>The percentage change is 74% and it is a percentage decrease</em>

2.\ Original = 160; New = 136

\%Change = \frac{136 - 160}{160} * 100\%

\%Change = \frac{-24}{160} * 100\%

\%Change = \frac{-24 * 100\%}{160}

\%Change = \frac{-2400\%}{160}

\%Change = -15\%

<em>The percentage change is 15% and it is a percentage decrease</em>

3.\ Original = 15; New = 12

\%Change = \frac{12- 15}{15} * 100\%

\%Change = \frac{-3}{15} * 100\%

\%Change = \frac{-3* 100\%}{15}

\%Change = \frac{-300\%}{15}

\%Change = -20\%

<em>The percentage change is 20% and it is a percentage decrease</em>

4.\ Original = 7; New = 10

\%Change = \frac{10- 7}{7} * 100\%

\%Change = \frac{3}{7} * 100\%

\%Change = \frac{3* 100\%}{7}

\%Change = \frac{300\%}{7}

\%Change = 43\% -- (approximated)

<em>The percentage change is 43% and it is a percentage increase</em>

<em></em>

5.\ Original = $30; New = $18

\%Change = \frac{18- 30}{30} * 100\%

\%Change = \frac{-12}{30} * 100\%

\%Change = \frac{-12* 100\%}{30}

\%Change = \frac{-1200\%}{30}

\%Change = -40\%}

<em>The percentage change is 40% and it is a percentage decrease</em>

6.\ Original = 9.6; New = 5.9

\%Change = \frac{5.9- 9.6}{9.6} * 100\%

\%Change = \frac{-3.7}{9.6} * 100\%

\%Change = \frac{-3.7* 100\%}{9.6}

\%Change = \frac{-370\%}{9.6}

\%Change = -39\% -- (approximated)

<em>The percentage change is 39% and it is a percentage decrease</em>

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