the graph shows g(x), which is a transformation of f(x) = |x|. write the function rule for g(x). \nwrite…

the graph shows g(x), which is a transformation of f(x) = |x|. write the function rule for g(x). \nwrite your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions.

the graph shows g(x), which is a transformation of f(x) = |x|. write the function rule for g(x). \nwrite your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions.

Answer

Explanation:

Step1: Identify vertex of ( g(x) )

The parent function ( f(x) = |x| ) has vertex at ( (0,0) ). The graph of ( g(x) ) also has vertex at ( (0,0) ), so ( h = 0 ) and ( k = 0 ).

Step2: Determine the value of ( a )

Take a point on ( g(x) ), e.g., ( (1, -1) ) (since when ( x = 1 ), ( y = -1 )). Substitute into ( g(x) = a|x - h| + k ) (with ( h = 0, k = 0 )):
( -1 = a|1 - 0| + 0 )
( -1 = a(1) )
So ( a = -1 ).

Step3: Write the function rule

Substitute ( a = -1 ), ( h = 0 ), ( k = 0 ) into ( a|x - h| + k ):
( g(x) = -1|x - 0| + 0 = -|x| )

Answer:

( g(x) = -|x| ) (or in the form ( -|x - 0| + 0 ))