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 left.Shift 2 units up

A.g(x)=|x-4|+2

B.g(x)=|x+2|+4

C.g(x)=|x+4|+2

D.g(x)=|x+2|-4

Got the answer its C.

Answer 1

Answer: C

Explanation:

The general form of the equation is: g(x) = a|x - h| + k ;

• "a" represents the vertical stretch (or shrink)
• "h" represents the x-coordinate of the vertex (left and right)
• "k" represents the y-coordinate of the vertex (up and down)

4 units left means h = 4

2 units up means k = 2

--> g(x) = |x - 4| + 2

Answer 2

Option: C is the correct answer.

C.
`g(x)=|x+4|+2`

Explanation:

The parent function f(x) is given by:

`f(x)=|x|`

Now, we know that for any parent function f(x) the transformation of the type:

f(x) → f(x+k)

is a translation of the function f(x) k units to the right if k<0

and k units to the left if k<0

and the transformation of the type:

f(x) → f(x)+k

is a translation of a function f(x) k units upward if k>0

and k units downward if k<0

Now here it is given that:

The function f(x) is shifted 4 units left and 2 units up.

Hence, the transformed function g(x) is given by:

`g(x)=f(x+4)+2\\\\i.e.\\\\g(x)=|x+4|+2`