Exercise 88 Page 250

We will describe the graph of g as a transformation of the graph of f. Then we will write a rule for g.

Describing the Transformation

To describe and graph the given transformation, g(x)=f(2x), let's look at the possible transformations. Then we can more clearly identify the ones being applied to the function f(x)=x^4+2x^3-4x^2.

Horizontal Stretch or Shrink
Horizontal stretch, 0< b<1 y=f( bx)	Horizontal shrink, b>1 y=f( bx)

In this case, there is a horizontal shrink of the graph of f(x) by a factor of 2. Therefore, we multiply x by 2. g(x)=f( 2x)

Finding the Rule for g(x)

Let's write the rule for g(x). To do so, we will substitute 2x for x in f(x).

g(x) = ( 2x)^4 +2( 2x )^3-4( 2x)^2

PowProdII

(a b)^m=a^m b^m

g(x) = 2^4 x^4 +2 (2^3) x^3 - 4 ( 2^2) x^2

CalcPow

Calculate power

g(x) = 16 x^4 +2 (8 ) x^3 - 4 ( 4 ) x^2

Multiply

Multiply

g(x) = 16 x^4 +16 x^3 - 16 x^2