30. f(x) = |x|; reflection in the y-axis followed by a
translation 3 units right

Step-by-step explanation:

We are given the parent function:

And we want to find the equation after a reflection in the y-axis followed by a translation of three units right.

To reflect a function over the y-axis, we multiply the input by a negative. That is:

In other words, a reflection over the y-axis will be given by:

To shift horzontally, we add if we are moving leftwards or subtract if we are moving rightwards. That is:

Where k is the horizontal translation.

Since we are translating three units rightwards, k = 3. Hence:

Recall that |ab| = |a||b|. Hence:

Hence, f reflected over the y-axis followed by a translation of three units right is given by:

y > 1/3x

y < = -x + 4

hope this : )

x=-7

step-by-step explanation:

x+3=-10

-10+3=-7

x=-7