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Write the equation for each transformation of f(x)= |x| described below.

Atranslate left 9 units, stretch vertically by a factor of 5, and translate down 23 units.

Btranslate left 12 units, stretch horizontally by a factor of 4, and reflect over the x-axis.

need steps don't understand how to do!

Verified Answer :

okay, original equation of an absolute value function is: 
a. f(x) = a |x-h| + k
a is the stretch or shrink
h is horizontal movement (watch the negative!!) 
k is vertical shift
 
Translate left 9 units means horizontal shift so the h changes. When you move to the left, the numbers become negative so y = a|x-(-9)| + k which becomes
 y = a|x+9| + k Then the vertical stretch of 5 becomes y = 5|x+9| + k And then a translation down 23 units means a negative shift down (which is your vertical shift) so:
f(x) = 5(x+9) - 23

b. translate left 12 units meaning a negative horizontal shift. y = a|x-(-12)| + k
so then it becomes y = a|x+12| + k
a stretch horizontally by 4 is your a, so y = 4|x+12| (you can just forget about the k since there is no vertical shift so your k = 0)
a reflection over the x-axis means that your horizontal axis is taken and folded and the reflection from the graph is your new graph. So basically, the whole equation becomes negative. 
y = -4|x+12|


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