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Doss [256]
3 years ago
13

Plzz help i have 5 minutes left, will mark brainliest!

Mathematics
1 answer:
Art [367]3 years ago
5 0

Answer:

g(x) = 2^{x-3} is the correct function equation that shows the corresponding transformation as shown in figure.

Step-by-step explanation:

Let us consider the function f(x) = bˣ. Lets add a constant c to the input of parent function i.e f(x) = bˣ. It would produce a horizontal translation move by c units, along x axis .

If c > 0, there will be translation to the "left" by "c" units.

If c < 0, there will be translation to the "right" by "c" units.

So, by analyzing the coordinate locations of the function f(x) = 2ˣ and g(x), it is clear that g(x) = 2^{x-3} is the correct function equation that shows the corresponding transformation. Because the g(x) also does has a translation to the 'right'.

It can be further verified as:

Lets check the coordinate locations of f(x) = 2ˣ and g(x) = 2^{x-3} at the the points y = 1, y = 2 and y = 4

At y = 1, the function f(x) = 2ˣ has the location at (0, 1) as 2ˣ = 2° ⇒ x = 0.

At y = 1, the function g(x) = 2^{x-3} has the location at (3, 1) as 2^{0} = 2^{x-3} ⇒ x-3 = 0 ⇒ x = 3. It has a translation to the "right".

At y = 2, the function f(x) = 2ˣ has the location at (1, 2) as 2ˣ = 2¹ ⇒ x = 1.

At y = 2, the function g(x) = 2^{x-3} has the location at (4, 2) as 2^{1} = 2^{x-3} ⇒ x-3 = 1 ⇒ x = 4. It has a translation to the "right".

At y = 4, the function f(x) = 2ˣ has the location at (2, 4) as 2ˣ = 2² ⇒ x = 2.

At y = 4, the function g(x) = 2^{x-3} has the location at (5, 4) as 2^{2} = 2^{x-3} ⇒ x-3 = 2 ⇒ x = 5. It has a translation to the "right".

So, it is clear that only g(x) = 2^{x-3} holds true and have a translation to the "right" by "c" units.

So, g(x) = 2^{x-3} is the correct function equation that shows the corresponding transformation as shown in figure.

Keywords: transformation, function

Learn more about transformation of function from brainly.com/question/5602886

#learnwithBrainly

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