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Svetradugi [14.3K]
2 years ago
8

Describe the transformations necessary to transform f(x) into g(x)

Mathematics
1 answer:
Aleks [24]2 years ago
6 0

Using translation concepts, the transformations are given as follows:

a) The function is horizontally compressed by a factor of 3 and shifted down one unit.

b) The function is shifted right 3 units and vertically stretched by a factor of 2.

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Item a:

The transformations are:

  • x -> 3x, hence the function is horizontally compressed by a factor of 3.
  • y -> y - 1, hence the function is shifted down one unit.

Item b:

The transformations are:

  • x -> x - 3, hence the function is shifted right 3 units.
  • y -> 2y, hence the function is vertically stretched by a factor of 2.

More can be learned about translation concepts at brainly.com/question/4521517

#SPJ1

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On a number line: Start at 0. Count forward until you reach 36. Once you've reached 36, Mark it. Then you go forward 57, from the mark you made at 36. You should end up on 93 on the number line.

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Round all the way 2689
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rounded to the nearest tens = 2690
rounded to the nearest hundreds = 2700
rounded to the nearest thousands = 3000

If the number before the place it needs to be round off is 5 and above, then it is rounded up. If the number is 4 and below, it is rounded down.

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4 years ago
Im giving 100 Points to anyone who could solve this for me please.
myrzilka [38]

Answer:

AB = 27.2

BC = 33.5

AC = 50.4

∠A = 38°

∠ABC = 112°

Step-by-step explanation:

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

\implies \sf \cos(30^{\circ})=\dfrac{29}{BC}

\implies \sf BC=\dfrac{29}{\cos(30^{\circ})}

\implies \sf BC=\dfrac{58\sqrt{3}}{3}=33.5\:(nearest\:tenth)

\implies \sf \tan(30^{\circ})=\dfrac{BD}{29}

\implies \sf BD=29\tan(30^{\circ})

\implies \sf BD=\dfrac{29\sqrt{3}}{3}

\implies \sf \sin(38^{\circ})=\dfrac{BD}{AB}

\implies \sf AB=\dfrac{\dfrac{29\sqrt{3}}{3}}{\sin(38^{\circ})}

\implies \sf AB=27.2\:(nearest\:tenth)

\implies \sf \tan(38^{\circ})=\dfrac{BD}{AD}

\implies \sf AD=\dfrac{\dfrac{29\sqrt{3}}{3}}{\tan(38^{\circ})}

\implies \sf AD=21.4\:(nearest\:tenth)

\implies \sf AC=AD+DC=21.4+29=50.4

The interior angles of a triangle sum to 180°

⇒ ∠A + 52° + 90° = 180°

⇒ ∠A = 180° - 90° - 52°

⇒ ∠A = 38°

⇒ ∠ABC + 38° + 30° = 180°

⇒ ∠ABC = 180° - 38° - 30°

⇒ ∠ABC = 112°

**I have checked the measures using a graphing programme - see attached**

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Step-by-step explanation:

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