Graphing Absolute Value Functions & Inequalities
f (x) = |3x-4|

absolute value makes everything positive instead of negative so since you didn't even really ask a question I'm just going to solve the problem without a point

f(x)=3x+4

f(x) = 3x - 4

f'(x) = x

x = 0

et

3x - 4 = 0

3x = 4

x = 4/3

3 * 0 - 4 = 0 - 4 = - 4

3 * 4/3 - 4 = 0

f(x) = I3x - 4I = I-4 ; 0I

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