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

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

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

need steps don't understand how to do!

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|