57.8k views
1 vote
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.

2 Answers

5 votes

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

User Kpw
by
7.9k points
5 votes

Answer:

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

User Nalo
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories