Let f(x)=8x and g(x)=8x+5+1.

Which transformations are needed to transform the graph of f(x to the graph of g(x)?

Select each correct answer.

horizontal translation 1 unit left

vertical translation 1 unit down

vertical translation 5 units up

vertical translation 1 unit up

horizontal translation 5 units right

horizontal translation 5 units left

If g(x) = (8x + 5) + 1, then the correct answers are in bold below

Select each correct answer.

horizontal translation 1 unit left

vertical translation 1 unit down

vertical translation 5 units up

vertical translation 1 unit up

horizontal translation 5 units right

horizontal translation 5 units left

Answer Link

MrRoyal MrRoyal · Answer 2 · 2021-12-03T04:53:20-05:00

Transformation involves changing the form of a function

The transformations are:

vertical translation 1 unit up
.
horizontal translation 5 units left.

The functions are given as:

\(\mathbf{f(x) = 8x}\)

\(\mathbf{g(x) = 8(x + 5) + 1}\)

Considering f(x), we have:

\(\mathbf{f(x) = 8x}\)

Start by translating the function 5 units left.

The rule of this translation is:

\(\mathbf{f'(x) = f(x + 5)}\)

So, we have:

\(\mathbf{f'(x) = 8(x + 5)}\)

Next, translate the function 1 unit up

The rule of this translation is:

\(\mathbf{f''(x) = f'(x) + 1}\)

So, we have:

\(\mathbf{f''(x) = 8(x + 5) + 1}\)

Rewrite as:

\(\mathbf{g(x) = 8(x + 5) + 1}\)

Hence, the transformations are: vertical translation 1 unit up and horizontal translation 5 units left