What are the key features of logarithmic and exponential graphs?
The exponential function, is formally known as the real function ex, where e is Euler's number, approximately 2.71828; this function has as a domain of definition the set of real numbers, and has the peculiarity that its derivative is the same function.
The logarithm, on the other hand, is the inverse function of the exponential.
how do transformations affect them?
Let's see this question with two examples
logarithm
f (x) = lnx original function
f (x) = - lnx reflection in x axis
f (x) = ln (x-2) displacement two units to the right.
f (x) = 2 + lnx displacement two units up
f (x) = ln (-x) refect in axis y
f (x) = ln (2-x) displacement two units to the right, reflection y
f (x) = - ln (-x) reflection in x, and in y axis
Exponential
f (x) = 5 ^ x original function.
f (x) = - 5 ^ x reflection on x axis
f (x) = 5 ^ -x reflection in axis y
f (x) = 5 ^ (x + 3) horizontal displacement 3 units to the left
f (x) = 5 ^ x +3 vertical displacement 3 units towards the top
f (x) = 5 ^ (x + 1) -4 displacement 1 unit to the left and 4 units to the bottom.
Answer:
900 cm²
Step-by-step explanation:
Perimeter of a rectangle is given by
P=2(l+w)
Where l and w are length and width respectively.
Substituting P with 120 cm
120=2(l+w)
Divide both sides by 2
60=l+w
Making w the subject of formula
w=60-l
Area, A=lw
Substitute w with 60-l
A=l(60-l)=60l-l²
Since A=60l-l²
Get the first derivative of A with respect to l
0=60-2l
l=60/2=30
Therefore, w=60-l=60-30=30
The length abd width are both 30cm. This is a square and a square is also a type of rectangle since it has four sides.
Area=30*30=900cm²
Answer: What number?
Step-by-step explanation:
Answer:
Option D. 
Step-by-step explanation:
we have
-----> the parent function
The vertex of the function F(x) is the origin (0,0)
The vertex of the function G(x) is the point (0,-1)
so
The rule of the translation is equal to
(x,y)------> (x,y-1)
That means ------> The translation is 1 unit down
Applying the rule of the translation to F(x)
F(x)-------> G(x)
Answer:
Suponiendo que te refieres a calcular el 28% de 375, tu respuesta es 105.
Step-by-step explanation:
y · 100 = 28 · 375
100y = 10500
100y ÷ 100 = 10500 ÷ 100
y = 105
