Two points on the graph of the linear function f are (0,3) and (3,9). Write a function g whose graph is a reflection in the x-axis of the graph of f.

Question

Two points on the graph of the linear function f are (0,3) and (3,9). Write a function g whose graph is a reflection in the x-axis of the graph of f.

Answer 1

Patrick missed one small thing

the slope is (9-3)/(3-0) = 6/3 = 2

B = y - mx = 9 - (2)(3) = 9-6 = 3

y = f(x) = 2x + 3. <-- this is correct

Reflection about x-axis, y changes sign. so (0,-3) and (3, -9) are on line g.

The slope is rise over run or (-9 - -3)/(3 - 0) = -6/3 = -2

B = y - mx = -3 - (-2)0 = -3

y = g(x) = -2x - 3

Answer 2

the slope is (9-3)/(3-0) = 6/3 = 2

B = y - mx = 9 - (2)(3) = 9-6 = 3

y = f(x) = 2x + 3

Reflection about x-axis, y changes sign. so (0,-3) and (3, -9) are on line g.

the slope is (-9 - -3)/(-3 - 0) = -6/-3 = 2

B = y - mx = -3 - (2)(0) = -3

g(x) = 2x-3