Let the graph of g be a horizontal shrink by a factor of 1/6 and a reflection in the x-axis, followed by a translation 2 units down of the graph of f(x)=x^2. Write a rule for g. g(x)=

Answer 1

A function s is the HORIZONTAL SHRINK of a function h by a factor k

if s(x) = h(kx)

It is called a shrink, because for k > 1 that has the effect of compressing

the function h towards the y-axis.

I find the problem statement a little confusing because

using k = 1/6 would result in stretching, not shrinking.

Therefore my guess is that the author means k = 6.

A function r is a REFLECTION of a function h in the x-axis

if r(x) = -h(x).

The reason is that r looks like a mirror image of h,

where the mirror is the x-axis.

A function t is a TRANSLATION 2 units down of a function h

if t(x) = h(x) - 2.

The graph of t looks like h, except shifted down 2 units.

Applying the definitions to your function f:

g(x) = -f(6x) - 2 = -36x^2 - 2

Answer 2

Starting with f(x) = x²

*Horizontal Shrink*

Assuming you are referring to compressing.

g(x) = 1/6 (x²)

This allows every value of x to be multiplied by 1/6, which then compresses the entire graph.

*Reflection across x-axis*

When doing a reflection over the x-axis we simply change the sign (Or multiple by -1)

g(x) = -1/6 (x²)

*Translating up*

When translating up or down, we add or subtract the value outside parenthesis

g(x) = -1/6 (x²)-2

Which this is our final answer, however, if the question asks us to translate to the right by 2 our answer would be:

g(x) = -1/6 (x²-2)

Hope this helps and just to repeat, I put your answer in bold!