Which transformations are needed to transform the graph of y = f(x) to g(x) = -f(x - 1) + 3

Lets's solve this step by step. Here we have a function:

So:

Step 1. Reflection across the x-axis:

Step 2. Shifting 1 unit to the right

Step 3. Shifting 3 unit up

Finally:

So the graph of f has been reflected across the x-axis, shifted 1 unit to the right and 3 units up to become the graph of g.

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

step-by-step explanation:

*calories burned = (weight)(calorie factor)*

calories burned = 180 (0.65)

calories burned = 117

the calories he used up is 117, which is 65% of his weight.