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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.

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MathPhys

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.

The h(x) should be Left 4 units

Calculation of h(x) that need to be translated:

Since

h(x) represent a line with slope 2.  

Let's assume it has y-intercept b.  

Therefore,

h(x) = 2x + b

d(x) represent h(x) shifted up 8 units.  

So,

d(x) = h(x) + 8

d(x) = 2x + b + 8

Now

h(x−a) = d(x)

2(x−a) + b = 2x + b + 8

2x − 2a + b = 2x + b + 8

-2a = 8

a = -4

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

Learn more about the function here: https://brainly.com/question/16995471

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