Algebra Problems

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

 

One: If F(x)=3x−∣3+x∣, find F(4) and F(−4).

F(4)= ____________

F(− 4)= ____________

 

 

 

Two: If f(x)=6x2−4x, 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)=

4              ifx≤−8

∣4x−4∣    if−8<x<3

4x+4      ifx≥3

find w(3) and w(−10).

w(3)= ____________

w(−10)= ____________

 

 

 

 

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

 

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

 

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

 

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

f(0)= ____________    and f(x)=−2 when x= ____________

 

Six:: Given w(t)=6+7t^2 and g(t)=7t−6, find (wg)(t).

Enter the expression in simplest form.

(wg)(t)= __________

 

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

(s w) (0)= __________

 

Eight: Find (w ∘ g)(1) for w(x)=7x^2−2x+8 and g(x)=2x−7.

(w ∘ g) (1)= ____________

Nine: Find (p ∘ p) (−1) for p(x)=3x^2+2x−3.

(p ∘ p) (−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 [  ]  c−1,500 [  ]  1,500c [  ]  c/1,500 [  ]

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

p(c)= c−9 [  ]  c−0.09 [  ]  0.09c [  ]  0.91c [  ]

Evaluate (r∘p)(c) and explain what the composition represents.

(r∘p)(c)= 0.91c−1,500 [  ]  0.09c−1,500 [  ]  0.91c−1,365 [  ]  0.91c+1,365 [  ]

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