Learning Check #3 (2nd semtester)

Target 1

100

Given f(x) and g(x) find the following :

f(x)=3x^2+1

g(x)=sqrt(x-1)

(f+g)(3)

32

200

Given f(x) and g(x) find the following:

f(x)=2x^2-4x+1

g(x)=3x+2

(f-g)(x)=

2x^2-7x-1

300

Given f(x) and g(x) find the following:

f(x)=3x^2+2

g(x)=2x+1

f(x)*g(x)=

6x^3+3x^2+4x+2

400

Given f(x) and g(x) answer the following:

f(x)=3x+4

g(x)=2x^2+3

(f@g)(-2)=

37

500

Given f(x) and g(x) answer the following:

f(x)=3x+4

g(x)=2x^2+3

g(f(x))=

18x^2+48x+35

Target 2

100

What test must you do to determine if the graph of a function can have an inverse?

Horizontal Line Test

200

What must the graph of a function pass to be considered a one-to-one function?

Both the horizontal and vertical line test

300

Given f(x), find the inverse of f(x):

f(x)=2x+3

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

400

Given f(x) and g(x), determine if the functions are inverses of each other using composition:

f(x)=3x+7

g(x)=1/3x+7/3

No

500

Find the inverse of 

f(x)=root(3)(x+2)

f^-1(x)=x^3-2

Target 4

100

Simplify: 

root(3)(192a^7b^3c^5)

4a^2bcroot(3)(3ab^2)

200

Simplify: 

root(4)((3a^3)/(27b^2c)

(root(4)(9a^3b^2c^3)/(3bc))

300

Simplify: 

(3-2sqrt5)(2+3sqrt5)

-24+5sqrt5

400

Simplify: 

(2+sqrt5)/(3-sqrt5

(11+5sqrt5)/4

500

Use your calculator to give me decimal approximation to the nearest three decimal places of : 

root(3)((1432)^2)+root(4)((15)^2)

130.919

Target 5

100

Rewrite the following using the small possible rational root: 

root(27)(c^9)

root(3)c

200

Rewrite the following using radicals with the smallest possible root:

(x^(1/12))^3

root(4)x

300

Simplify the following using and write using the smallest possible root:

root(4)((81b^3)^3

27b^2sqrtb

400

Simplify the following using rational exponents to the smallest possible root:

(x^(1/3)y^(2/5))/(x^(2/3)y^(1/5))

(y^(1/5))/x^(1/3)

500

Simplify the following using rational exponents to the smallest possible root:

(x^(4/3)y^(-1/2))/(x^(-1/4)y^(1/3))

(x^(19/12))/(y^(5/6))

Howard's Choice

100

What is the parent function of: 

f(x)=sqrtx-4

f(x)=sqrtx

200

How does the function shift from its parent function:

f(x)=sqrt(x+4)-3

Down three and left 4

300

Describe the end behavior of the following function without using your calculator:

f(x)=x^4-3x^5

As x=>oo, f(x)=>-oo

As x=>-oo, f(x)=>oo

400

Given 3, -2, and 4 are zeros of a function, find the specific function goes through the point (1,2).

f(x)=-1/9(x-3)(x+2)(x-4)

500

Find all the zeros of 

f(x)=x^3-2x^2+4x-8

x=2, 2i, -2i