Question

If you apply the changes below to the absolute value parent function, f(x) = |x|, what is the equation of the new function?Shift 4 units to the right.Shift 6 units up.

A. g(x) = |x – 4| + 6

B. g(x) = |x – 6| + 4

C. g(x) = |x + 6| + 4

D. g(x) = |x + 4| + 6

Answer 1

g(x)=|x-4|+6

answer: A





Regards M.Y.

Answer 2

The equation of the new function will be  $g(x) = |x-4|+6$, i.e. option (A) .

What is transformation  ?

Transformation is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X.

We have,

$f(x) = |x|$

And

It shifted $4$ units to the right and $6$ units up.

And the parent quadratic function is in the form of $f(x)=a(x-h)^2+k$

Here,

"$h$" tells if the vertex of the parabola is going left or right.

"$k$" determines if the vertex of the parabola is going up or down.

So, According to the question;

We have,

$(a)$  $4$  units to the right

$(b)$  $6$  units up

So, Equation $f(x) = |x|$ have moved the vertex of the parabola $4$   units to the right and $6$ units up.

Now,

$f(x)=a(x-h)^2+k$

$f(x) = |x|$

Now,

Shifting right means adding $4$  i.e. $h=4$ and going up means adding i.e. , $k=6$,

So,

$f(x) = |x|$

$g(x) = |x-4|+6$

Hence, we can say that the equation which represents the transformation of $f(x) = |x|$ , is given by  $g(x) = |x-4|+6$, i.e. option (A) .

To know more about transformation click here

https://brainly.com/question/10059147

#SPJ2