Find the domain (d) range(r) and asymptote (a) of the graph f(x)=5^x+6

D= R

R =(6,∞)

A: y=6

Step-by-step explanation:

We are asked to Find the domain (D ) range(R) and Asymptote (A) of the graph

Our function is an translated function of

which is an exponential function. Therefore the basic properties remains the same.

Any exponential function is defined for all values of x and Hence

c

however, The range of exponential functions is always positive from 0 to infinity . however here we have 6 added to out parent exponential function and hence the Range of exponential function is always be

Range = (6,∞)

Asymptote : Asymptote of our parent exponential  function is y = 0, but in our function , the asymptote will be y=6

x= -3

step-by-step explanation:

step 1: simplify brackets

4 - x - 1 = 6

step 2: simpilfy

3 - x = 6

step 3: subtract 3 from both sides

-x = 6 - 3

step 4: simpilfy 6 - 3

-x = 3

step 5: multiply both sides by -1

x = -3

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)