(g + h)(n) =
g(n) + h(n) =
2n + n^2 + 5 =
n^2 + 2n + 5 (standard form)
To simplify the function, we need to know some basic identities involving exponents.
1. b^(ax)=(b^x)^a=(b^a)^x
2. b^(x/d) = (b^x)^(1/d) = ((b^(1/d)^x)
Now simplify f(x), where
f(x)=(1/3)*(81)^(3*x/4)
=(1/3)(3^4)^(3*x/4) [ 81=3^4 ]
=(1/3)(3^(4*3*x/4) [ rule 1 above ]
=(1/3) (3^(3*x)
=(1/3)(3^(3x)) [ or (1/3)(27^x), by rule 1 ]
(A) Initial value is the value of the function when x=0, i.e.
initial value
= f(0)
=(1/3)(3^(3x))
=(1/3)(3^(3*0))
=(1/3)(3^0)
=(1/3)(1)
=1/3
(B) the simplified base base is 3 (or 27 if the other form is used)
(C) The domain for an exponential function is all real values ( - ∞ , + ∞ ).
(D) The range of an exponential function with a positive coefficient and without vertical shift is ( 0, + ∞ ).
That is false. When you look at a number line, -3 is to the left of -2. A number to the left of another number is less than the number to the right.
Given cost function C(a) = 7.5a, where a is the number of T-shirts.
Let us complete table.
We need to plug a=1,2,3,4 in above function to get the costs to complete the table.
For a =1
C(1)= 7.5(1) = 7.50
For a =2
C(2)= 7.5(2) = 15.00
For a =3
C(3)= 7.5(3) = 22.50
For a = 4
C(4)= 7.5(1) = 30.00
In order to find the common difference we need to find the diffrences of costs 15-7.50 = 7.50
22.50-15.00=7.50.
<h3>Therefore, common difference is 7.5.</h3>
a represents the number of T-shirts.
Domain of a is the numbers we can take for a.
So, we can take value for a as 0 or greater value.
Therefore, domain for a would be a is gerater than or equal to 0.
<h3>Domain : a≥0</h3>
If you have 20/10, that equals 2. Then if you move the decimal place over 1 place then you have 2. If you divide 2 again by 10, then move the decimal place over in another place, it is equaling 0.2.
