Question

The function ƒ(x) = is translated 3 units in the positive y-direction and reflected across the y-axis. Select the correct equation for the resulting function.

Multiple choice answers in attachment image

Answer 1

Answer:

A) ƒ(x) =  + 3

Step-by-step explanation:

A. f(x)=−x+3

Explanation:

It is stated that the function f(x) is translated 3 units in the positive y-direction. This means that the function f(x) is moved 3 units upwards.

In transforming functions, a upwards vertical translation (moving the function upwards) of a units is done by: f(x) + a.

This means that in order to move f(x) 3 units upwards, we need to add 3 to the given function. This now makes our function:

f(x)=x+3

Finally, it is also stated that it is reflected across the y-axis. For reflection across the y-axis, the transformation can be done by simply multiplying -1 to x only

f(x)=−1×x+3

f(x)=−x+3

Therefore, the answer is A

Answer 2

The function that is translated and reflected across y-axis, will be f(x) = √(-x) + 3. Then the correct option is A.

What is a transformation of geometry?

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry. But flip the image.

Translation does not change the size and shape of the geometry. But change the location of the shape.

The function is given below.

f(x) = √x

The function is translated 3 units in the positive y-direction. Then add 3 in the function. Then the function will be  

f(x) = √(x) + 3

Then the function is reflected across the y-axis. Then replace x with the negative x, then the function will be

f(x) = √(-x) + 3

The function is translated 3 units in the positive y-direction and reflected across the y-axis, then the function will be f(x) = √(-x) + 3.

Then the correct option is A.

More about the transformation of geometry link is given below.

https://brainly.com/question/22532832

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