# Algebra Problems

May 23, 2015

Please look over each problem to see if it makes sense to you prior to bidding. Thank you.

One: If F(x)=3xâˆ’âˆ£3+xâˆ£, find F(4) and F(âˆ’4).

F(4)= ____________

F(âˆ’ 4)= ____________

Two: If f(x)=6x2âˆ’4x, find f(2+z).

Enter the expression in simplest form. The terms of the expression must be entered in descending order of degree.

f(2+z)= __________

Three (steps for this would be great) : If

w(x)=

4Â Â Â Â Â Â Â Â Â Â Â Â Â  ifxâ‰¤âˆ’8

âˆ£4xâˆ’4âˆ£Â Â Â  ifâˆ’8<x<3

4x+4Â Â Â Â Â  ifxâ‰¥3

find w(3) and w(âˆ’10).

w(3)= ____________

w(âˆ’10)= ____________

 Â

Four: Write the domain and range of the function using interval notation.
(a) Write the domain

 (a) (âˆ’2,3] (b) [âˆ’2,3) (c) [3,8) (d) R (e) [3,8] (f) [âˆ’1,8]
(b) Write the range

 (a) R (b) (3,8) (c) [âˆ’1,8] (d) [3,8] (e) (âˆ’2,3) (f) [âˆ’2,3]

five: Using the graph, find f(0) and find x such that f(x)=âˆ’2.

f(0)= ____________Â Â Â  and f(x)=âˆ’2 when x= ____________

Six:: Given w(t)=6+7t^2 and g(t)=7tâˆ’6, find (wg)(t).

Enter the expression in simplest form.

(wg)(t)= __________

Seven: Given s(x)=âˆ’2x^2 and w(x)=3x+3, find (s w)(0).

(s w) (0)= __________

Eight: Find (w âˆ˜ g)(1) for w(x)=7x^2âˆ’2x+8 and g(x)=2xâˆ’7.

(w âˆ˜ g) (1)= ____________

Nine: Find (p âˆ˜ p) (âˆ’1) for p(x)=3x^2+2xâˆ’3.

(p âˆ˜ p) (âˆ’1)= ____________

Ten: A car dealership offers a \$1,500 factory rebate and a 9% discount off the price of a new car c.

Write a functionr for the cost of the car after receiving only the factory rebate.

r(c)= c+1,500 [Â Â ]Â Â câˆ’1,500 [Â Â ]Â Â 1,500c [Â Â ]Â Â c/1,500 [Â Â ]

Write a function p for the cost of the car after receiving only the dealership discount.

p(c)= câˆ’9 [Â Â ]Â Â câˆ’0.09 [Â Â ]Â Â 0.09c [Â Â ]Â Â 0.91c [Â Â ]

Evaluate (râˆ˜p)(c) and explain what the composition represents.

(râˆ˜p)(c)= 0.91câˆ’1,500 [Â Â ]Â Â 0.09câˆ’1,500 [Â Â ]Â Â 0.91câˆ’1,365 [Â Â ]Â Â 0.91c+1,365 [Â Â ]

(râˆ˜p)(c) represents the cost of the car when the __________ is applied first and then the __________ is applied.

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Category: Mathematics

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