For each function do the following Factor the function if ne

For each function do the following: Factor the function (if necessary) Identify the zeros of the function. Identify where the function is undefined (if anywhere). y = 2x^-1/2 - 2x y = x + 2x ln x y = 3x^2 - 12 y = 4x^3 - 12x^2

Solution

y = 2x^-1/2 - 2x

taking the gcf out

2x^-1/2 ( 1 - x^3/2)

to find zeros of the function set the function equal to zero

2x^-1/2 ( 1 - x^3/2) = 0

x = 1

the function is undefined at x = 0

2) y = x+ 2x ln x

taking out the gcf

x( 1+ 2ln x)

setting the expression to zero

x( 1+ 2ln x) = 0

x = 0

1+2ln x = 0

ln x = -1/2

x = e^-1/2 = .607

the function is undefined for x<=0

3) y = 3x^2 - 12

taking out the gcf

3(x^2 - 4 )

zeros are

3(x^2 - 4 ) = 0

x^2 - 4 =0

x = + - 2

function is defined for all x

4) y = 4x^3 - 12x^2

taking out the gcf

4x^2 ( x - 3)

finding the zeros

4x^2 ( x - 3) = 0

x = 0

x = 3

function is defined for all x