What set of reflections would carry hexagon abcdef onto itself?

a. y=x, x-axis, y=x, y-axis
b. x-axis, y=x, x-axis, y=x
c. y-axis, x-axis, y-axis
d. x-axis, y-axis, y-axis

option a. y=x, x-axis, y=x, y-axis.

Explanation:

1) Take a general point with coordinates (a,b)

2) Reflecting it over the line y = x translates it to (b,a)

3) Reflecting (b,a) over the x-axis translates it to (b,-a)

4) Reflecting (b,-a) over y = x translates it to (-a,b)

5) Reflecting (-a,b) over the y-axis translates it to (a,b)

Therefore, that set of reflections have translated (a,b) to the same place (a,b), concluding that that set of reflections carries the hexagon ABCDEF onto itself.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.