(20 POINTS) The graph of f(x)= |x| is translated 2 units to the left and then horizontally stretched by a factor of 2. Determine the equation of the final graph.

g(x) = Ix/2 + 1I

Step-by-step explanation:

First, let's describe the transformations in a general way.

Horizontal translation.

For a function f(x) a horizontal translation of N units is written as:

g(x) = f(x + N)

if N is positive, the translation is to the left.

If N is negative, the translation is to the right.

Horizontal stretch.

For a function f(x) a horizontal stretch of scale factor k is written as:

g(x) = f(x/k)

Then if we have the function f(x) = IxI

First we do a translation of 2 units to the left, then we have N = 2

The transformation is:

g(x) = f(x + 2)

Now we do a horizontal stretch by a factor of 2.

g(x) = f( (x + 2)/2=

g(x) = f( x/2 + 1) = Ix/2 + 1I

The equation of the final graph is:

g(x) = Ix/2 + 1I

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: