Write an equation g(x) for the parent function f(x)=x^2 re-elected in the x-axis, stretched by a factor of 7, shifted left 5 units, and shifted down 2 units

The resulting equation is .

Step-by-step explanation:

is obtained by making three operation on parent function , whose procedured is presented below:

Streching

, where

Horizontal shift

, where when is translated leftwards (+x direction), otherwise it is translated rightwards (-x direction).

Vertical shift

, where when is translated upwards (+y direction), otherwise it is translated downwards. (-y direction)

If , then is:

Stretching

Horizontal shift

Vertical shift

The resulting equation is .

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