Use the four functions below for this question:

f(x)

x f(x)

−1 -7

1 1

2 5

g(x)
(graph)

a line going through the point, negative 2, 5, and 0, negative 3

h(x)

h(x) = −4x + 3

j(x)
cameron adds 4 new hats to his collection each year. he started with only 3.

question below

compare and contrast these four functions using complete sentences. focus on the slope and y-intercept first, and then on any additional properties of each function

Let us first obtain the standard form of each equation:

f(x): | using points (1,1) and (2,5)

y - 1 = [(5-1)/(2-1)] (x - 1)
y - 1 = 4x - 4
y = 4x - 3

g(x) : | using points (-2,5) and (0,-3)

y - 5 = [(-3-5)/(0+2)] (x + 2)
y - 5 = -4x -8
y = -4x - 3

h(x) = -4x + 3

j(x) = 4x + 3

In summary:

f(x) = 4x - 3
g(x) = -4x - 3
h(x) = -4x + 3
j(x) = 4x + 3

f(x) and j(x) both have the same slope, but start on different y-ordinates. g(x) and h(x) have the same slope, which is the negative of the slope of f(x) and j(x).