6 Consider the square reciprocal function fx Write the equat

6) Consider the square reciprocal function f(x) Write the equation of the function under the following transformations (no need to graph) a. Shift the graph to the left 4 units and up 6 units (4 points) b. Reflected over the x-axis and horizontally compressed by a factor of 2 (4 points) c. shifted right 1 unit, reflected over the y axis, vertically compressed by a factor of 5 and shifted down 3 units (8 points)

Solution

f(x) = 1/x^2

a) Shift 4 units left and 6 units up:

Shift 4 units left

f1(x) = 1/(x+4)^2

Shift 6 units up

f2(x) = 1/(x+4)^2 +6

b) Reflect over x axis

f1(x) = -1/x^2

horizontally compressed by a factor of 2

f2(x) = -1/(2x)^2 = -1/4x^2

c) Shift right 1 unit

f1(x) = 1/(x-1)^2

Reflect over y axis

f2(x) = f(-x) = 1/(-x-1)^2

Vertically compressed by a factor of 5

f3(x) = (1/5)f(x) = (1/5)*(1/(-x-1)^2 = 1/5(-x-1)^2

Shifted down by 3 units:

f4(x) = f(x) -3 =  1/5(-x-1)^2 -3