"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 [tex]f(x)=a(b)^{x}[/tex], where
∵ [tex]f(x)=2(\frac{1}{4})^{x}[/tex]
- Compare it with the form above
∴ a = 2 ⇒ initial value
∴ b = [tex]\frac{1}{4}[/tex] ⇒ 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 [tex]y=2(\frac{1}{4})^{-x}[/tex]
- 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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