Question

Which best describes the range of the function f(x) = 2(one-fourth) Superscript x after it has been reflected over the y-axis?

Answer 1

"All real numbers greater than 0" best describes the range of the function after it has been reflected over the y-axis ⇒ 3rd answer

Step-by-step explanation:

The form of the exponential function is $f(x)=a(b)^{x}$, where

• a is the initial value (value f(x) at x = 0)
• b is the growth/decay factor
• The domain of the function is {x : x ∈ R} (all real numbers)
• The range of the function is {y : y > 0} (all positive real numbers)

∵ $f(x)=2(\frac{1}{4})^{x}$

- Compare it with the form above

∴ a = 2 ⇒ initial value

∴ b = $\frac{1}{4}$ ⇒ decay factor because its between 0 and 1

∵ The domain of the function is the values of x

∴ The domain of the function is {x : x ∈ R} ⇒ all real numbers

∵ The range of the function is values of y

∴ The range of the function is {y : y > 0}

∵ Reflection over the y-axis change the sign of x

∴ The image of f(x) is $y=2(\frac{1}{4})^{-x}$

- That means, all x-coordinates of the points on the graph

   opposite in signs, but that does not effect the domain

   because the domain is all real numbers

∵ There is no change of the sign of y

- That means reflection over y-axis does not effect the range

∴ The range of the function after reflection is the same as the

    range of f(x)

∴ The range of the image of f(x) is {y : y > 0}

"All real numbers greater than 0" best describes the range of the function after it has been reflected over the y-axis

Learn more:

You can learn more about the reflection in brainly.com/question/4057490

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Answer 2

Answer:

Answer is C

Step-by-step explanation: