What transformations of the parent function f(x) = |x| should be made to obtain the graph f(x) = -|x| - 5?

Transformation: Reflect across x-axis and then shift 5 unit down

Step-by-step explanation:

We are given parent function, f(x)=|x|

We need to made by translation, f(x)=-|x|-5

It is absolute function.

Here we have two transformation.

f(x)=|x|  changes to f(x)=-|x|

f(x) will reflect about x-axis because y value change.

If we compare both the function. -5 subtract from f(x)

If f(x) → f(x) + a then

f(x) shift vertical

If a>0 then shift up

If a<0 then shift down.

Thus, f(x) will shift 5 units down from parent function.

We can see in graph. Please see the attachment for graph.

addition

step-by-step explanation:

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2