Algebra Answers

Use the parent function f(x) and the description of the transformation to write the new function h(x).

Reflect the graph of f(x) = 2x − 5 across the y−axis and then translate it 2 units down.

[(4x^6)^3(4y^-8)/ (2x)^4(12y^3)^2]^1/2

Q1)MR. ANG INVESTED $865 IN A BUSINESS MAKING GIFT BASKETS. HE MAKES $13.28 FOR EACH GIFT BASKET THAT HE SELLS. WRITE A FUNCTION THAT REPRESENTS THE SITUATION. HOW MANY GIFT BASKETS MUST MR. ANG SELL UNTIL HE MAKES A PROFIT?'
Q2) The number of bacteria cells in a culture can be modelled by the function B(t)= -0.03(t-4)^2+12

You have given a function λ : R → R with the following properties (x ∈ R, n ∈ N):

λ(n) = 0 , λ(x + 1) = λ(x) , λ(n+1/2)=1
Find two functions p, q : R → R with q(x)6=0 for all x such that λ(x) = q(x)(p(x) + 1).

Determine the roots of the function f(x) = (5^(2x) − 6)^2 − (5^(2x) − 6) − 12

Find all points (x, y) where the functions f(x), g(x), h(x) have the same value :
f(x) = 2^(x−5) + 3 , g(x) = 2x − 5 , h(x) = (8/x)+ 10

Find all points (x, y) where the functions f(x), g(x), h(x) have the same value :
f(x) = 2x−5 + 3 , g(x) = 2x − 5 , h(x) = (8/x)+ 10

Consider the following sequence of successive numbers of the 2^k-th power:
1, 2^2^k, 3^2^k, 4^2^k, 5^2^k, ...
Show that the difference between the numbers in this sequence is odd for all k ∈ N

(e^x)^2=e^2x prove this identity