The graphs below have the same shape. what is the equation of the red graph?

we have

the vertex of the function g(x) is the point

the vertex of the function f(x) is the point

so

the rule of the translation of g(x) to f(x) is

(x,y)------> (x,y-4)

that means

the translation is units down

therefore

the equation of the function f(x) is

therefore

the answer is

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

b.an increase in a causes b to decrease