Graph the function and identify the domain and range y=-3x^2

Domain : ( -∞ , ∞ ) ; range ( -∞ , ∞ ]

Step-by-step explanation:

Given :  y=-3x².

To find :  Identify the domain and range .

Solution : We have given that  y = -3x².

Domain :  the domain of the function is the set of input values for which function is defined .

So, the function is defined for all real values .

Notation : ( -∞ , ∞ )

Range : The set of values of dependent variable for which function is defined .

Range  for quadratic function is always less than or equal to 0 .

Notation : ( -∞ , ∞ ]

Therefore , Domain : ( -∞ , ∞ ) ; range ( -∞ , ∞ ]

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752