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, + ∞ ).
Answer: 28:9
Step-by-step explanation:
56:18
56÷2=28
18÷2=9
=28:9
Table (A) represents the parabola y = x² - 6x in which the parabola opens and the y-intercept is (0, 0) table (A) is the correct choice.
<h3>What is a parabola?</h3>
It is defined as the graph of a quadratic function that has something bowl-shaped.
We have the tables shown in the picture.
We know the quadratic form of a parabola is:
y = ax² + bx + c
If a > 0 the parabola opens
In the equation:
y = x² - 6x
1 > 0 the parabola opens and y-intercept is:
y = 0 (plug x = 0 in the given equation)
a = 1, b = -6, and c = 0
Thus, table (A) represents the parabola y = x² - 6x in which the parabola opens and the y-intercept is (0, 0) table (A) is the correct choice.
Learn more about the parabola here:
brainly.com/question/8708520
#SPJ1
Answer:
clean
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation: