If f(x) = x3 and g(x) = (x + 1)3, which is the graph of g(x)?
a. a vertical transformation of f(x) 1 unit upward
b. a horizontal transformation of f(x) 1 unit to the left
c. a horizontal transformation of f(x) 1 unit to the right
d. a vertical transformation of f(x) 1 unit downward
e. a vertical transformation of f(x) 3 units downward

The correct option is b.

Step-by-step explanation:

The given function are

From the given function,we get

               .... (1)

The transformation of f(x) is defined as

         ... (2)

Where, a represents the horizontal shift and b represents the vertical shift.

If a>0, the graph of f(x) shifts a units left and if a<0, the graph of f(x) shifts a units right.

If b>0, the graph of f(x) shifts b units upward and if b<0, the graph of f(x) shifts b units downward.

On comparing (1) and (2), we get

Since a=1>0, therefore the graph of g(x) is a horizontal transformation of f(x), 1 unit to the left. Option b is correct.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.