Transformations of Linear Functions

Linear Parent Function

Most basic linear function, f(x) = x.

Slope

Rate of change of a linear function.

Y-Intercept

Point where the line crosses the y-axis.

Vertical Shift

Transformation moving the graph up or down.

g(x) = f(x) + 3

Translates f(x) vertically up by 3 units.

g(x) = f(x) - 3

Translates f(x) down by 3 units.

h(x) = f(x) + 4

Graph shifts up 4 units from f(x).

h(x) = f(x) - 5

Graph shifts down 5 units from f(x).

Horizontal Shift

Transformation moving the graph left or right.

g(x) = f(x - 3)

Translates f(x) right by 3 units.

g(x) = f(x + 3)

Translates f(x) left by 3 units.

m(x) = f(x - 1)

Graph shifts right 1 unit from f(x).

r(x) = f(x + 7)

Graph shifts left 7 units from f(x).

g(x) = f(x - 5)

Graph shifts right 5 units from f(x).

a(x) = f(x - 9)

Graph shifts right 9 units from f(x).

g(x) = f(x) - 7

Represents function b, shifted down 7 units.

c(x) = f(x) + 5

Represents a vertical shift up 5 units.

c(x) = f(x + 5)

Represents a horizontal shift left 5 units.