Which function has a range of all real numbers greater than or equal to -4?​ A. f(x) = x-4
B. f(x) = -4x
C. f(x) = (x+1)^2 - 4
D. f(x) = -|x-3|-4​

C.  

Step-by-step explanation:

A. the graph is a straight line with slope 1.  It goes up/down infinitely far so the range is all real numbers.  Not A!

B. The graph is a straight line with slope -4, so, like the function in A, the range is all real numbers.  Not B!

D. The graph is an absolute value function  y = |x|, reflected over the x-axis, shifted right 3 units, then shifted down 4 units.  So the graph starts witha "vee" shape opening up, becomes a vee opening down, then ultimately gets shifted down 4 units.  The range is all real numbers less than or equal to -4.

See the attached graphs.  image2 is the function in answer choice D.

answer: the answer is e

step-by-step explanation:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)