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Irina-Kira [14]
1 year ago
15

Let f(x)= lxl-3 Write a function g whose graph is a translation 5 units down of the graph of f.

Mathematics
1 answer:
soldier1979 [14.2K]1 year ago
4 0

If the function "f(x) = lxl-3" were translated five units down the graph, g(x) would be lxl-8.

We must be familiar with function transformation and different forms of transformation in order to properly understand the question. When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects" to create a new function. For instance, by simply pushing the graph of the function g(x) = x2 up by 7 units, the graph of the function f(x) = x2 + 7 is generated. It is advantageous to convert a function since it saves us from having to create a new function from begin. Function transformations typically fall into one of three categories: 1. 2nd translation 3. dilation Reflection

The given query is about Translation of Function. To create a new function, translation moves the curve up or down and modifies its position. Translation comes in two flavours. Vertical and horizontal translation.

When the curve changes, "the function" shifts upward or downward. By doing this, a function of the form y = f(x) is transformed into f(x) ± k, where k stands for the vertical translation. In this case, the function moves up by k units if k > 0.

The function goes down by 'k' units if k < 0.

The curve in the given problem goes down by 5 units, so k = 5. Which is a vertical translation scenario. Consequently, y = f(x) becomes f(x) - k = g(x) and g(x) = f(x) - k = lxl-3 -5 = lxl - 8.

Therefore the new function after translation is g(x) =  lxl - 8.

Learn more about function and types of transformation such as translation, dilation etc here

brainly.com/question/26092237

#SPJ9

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Step-by-step explanation:

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Applying value in (i) we get

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7 0
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4 0
3 years ago
Tickets at a play cost $10 or $14. If 800 tickets were sold and $9,040 was collected by the box office, how many $14 tickets wer
pav-90 [236]
STEP 1:
determine equations needed

x= # of $10 tickets
y= # of $14 tickets

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x + y= 800

COST EQUATION
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STEP 2:
multiply quantity equation by -14

-14(x + y)= -14(800)
-14x - 14y= -11,200


STEP 3:
add new quantity equation in step 2 to cost equation of step 1 to solve for x using elimination

-14x - 14y= -11,200
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y term cancels out

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divide both sides by -4

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STEP 4:
substitute x value in step 3 into either original equation

x + y= 800
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subtract 540 from both sides

y= 260 fourteen dollar tickets


ANSWER: There were 540 $10 tickets and 260 $14 tickets sold.

Hope this helps! :)
5 0
3 years ago
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