Given that f(x) = |x| is the parent of g(x) = |x−2|+1 what transformations have occurred on the graph from f(x) to g(x)? question 2 options: horizontal shift left 2 and a vertical shift up 1. horizontal shift right 2 and a vertical shift down 1. horizontal shift right 2 and a vertical shift up 1. horizontal shift left 2 and a vertical shift down 1.

Horizontal shift Right 2 and a Vertical shift Up 1.

Step-by-step explanation:

Given that f(x) = |x| is the parent of g(x) = |x−2|+1

g(x)= |x=2|+1

Now we compare it with f(x)

+1 is added at the end

when any number is added at the end then there will be a vertical shift up

when any number is subtracted at the end then there will be a vertical shift down

Here 1 is added at the end , so vertical shift up by 1 unit

If any number added with x , there will be a horizontal shift to the  left

If any number subtracted  with x , there will be a horizontal shift to the right

In g(x) , 2 is subtracted with x  , so horizontal shift 2 units to the right

20

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is