For the function g defined by g(x)= 55 x +3x find g(−x),−g(x), and −g(−x).
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According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.
<h3>How to apply translations on a given function</h3>
<em>Rigid</em> transformations are transformation such that the <em>Euclidean</em> distance of every point of a function is conserved. Translations are a kind of <em>rigid</em> transformations and there are two basic forms of translations:
Horizontal translation
g(x) = f(x - k), k ∈ (1)
Where the translation goes <em>rightwards</em> for k > 0.
Vertical translation
g(x) = f(x) + k, k ∈ (2)
Where the translation goes <em>upwards</em> for k > 0.
According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.
To learn more on translations: brainly.com/question/17485121
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<u>Answer:</u>
- Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.
<u>Step-by-step explanation:</u>
We know that:
- 48 + 8(b) = Carly's expenditure
- 10(b) = Carly's expenditure
- 48 + 8b = 10b
- B = Boxes of cards
<u>Work:</u>
- 48 + 8b = 10b
- => 48 + 8b - 8b = 10b - 8b
- => 48 = 2b
- => b = 24
<u>Now, let's substitute the value of b into any equation.</u>
- 10(24)
- => 240
<u>Hence, Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.</u>
Hoped this helped.