Select all the correct answers. Consider functions fand g.
f(x) = 4(x – 3)2 + 6
g(x) = -2(x + 1)2 + 4
Which statements are true about the relationship between the functions?
The vertex of function gis 4 units to the left of the vertex of function f.
The vertex of function gis 2 units below the vertex of function f.
Function gopens in the same direction as function f.
Function gopens in the opposite direction of function f.
The vertex of function gis 2 units above the vertex of function fi
vertex of function gis 4 units to the right of the vertex of function f.

Step-by-step explanation:

f(x) = 4(x-3)² + 6

Up-opening parabola with vertex (3, 6)

g(x) = -2(x+1)² + 4

Down-opening parabola with vertex (-1,4)

A. True

B. True

C. False

D. True

E. False

F. False

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

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