5. what’s the transformations change the graph of f(x) to the graph of g(x)?
f(x)=x^2
g(x)=(x+3)^2-7
a) the graph of g is the graph of f translated the the right 3 units and up 7 units.
b) the graph of g is the graph f translated to the left 3 units and down 7 units.
c) the graph of g is the graph f translated up 3 units and the the left 7 units
d) the graph of g is the graph f translated down 3 units and to the right 7 units.

B

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift to the left of a units

• If a < 0 then a shift to the right of a units

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Given

f(x) = x², then

g(x) = (x + 3)² - 7

is a shift to the left of 3 units and down 7 units → B

1/800 is the right answer

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.