The slope of a linear function h (x) is 2. Suppose the function is translated 8 units up to get d (x). How can h (x) be translated to the left or right to represent the same function d (x) ? Explain your answer.

Left 4 units

Step-by-step explanation:

h (x) is a line with slope 2. Let's say it has y-intercept b. So:

h (x) = 2x + b

d (x) is h (x) shifted up 8 units. So:

d (x) = h (x) + 8

d (x) = 2x + b + 8

We want to shift h (x) left or right to get d (x). If we say that shift is a units to the right, then:

h (x-a) = d (x)

2 (x-a) + b = 2x + b + 8

2x - 2a + b = 2x + b + 8

-2a = 8

a = - 4

a is negative, so the shift is to the left.

h (x) should be shifted to the left 4 units.