Show your work to receive credit. graph each pair of functions on the same coordinate plane. describe a transformation that changes f(x) to g(x). f(x) = -x -2 g(x) = x + 3

Step-by-step explanation:

The two functions have opposite slope, so reflection across a horizontal line will change one to the other. The line of reflection will be the horizontal line through the point of intersection of these functions. The y-value of that point is halfway between the y-intercepts -2 and +3, so is 1/2.

The transformation can be described by ...

... g(x) = -(f(x) -1/2)) +1/2 . . . . reflection across the line y = 1/2

... g(x) = -f(x) +1 . . . . . . . . . . . simplified

Check

... g(x) = -(-x-2) +1 = x+2+1 = x+3 . . . . yes

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Alternate solution

The functions could also be a reflection of each other across the vertical line through their point of intersection at x=-5/2.

... g(x) = f(-(x +5/2) -5/2)

... g(x) = f(-x-5) . . . . . . . . . . simplified

Check

... g(x) = -(-x-5) -2 = x+5-2 = x+3 . . . . yes

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

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