Select all the correct answers.
consider the graph of function g below.
determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g.

Options a, c and d

Step-by-step explanation:

Given the parent function f(x) = x, and calling g(x) its transformation. In the plot we see the following equation: -3*x -1

Option a

reflect over the y-axis: g(x) = -x

then vertically stretch by a factor of 3: g(x) = -3*x

and then shift down 1 unit: g(x) = -3*x -1

Option b

Shift left 2 units: g(x) = x + 2

then reflect over the x-axis: g(x) = -x - 2

and then vertically stretch by a factor of 3: g(x) = -3*x - 2

Option c

reflect over the x-axis: g(x) = -x

then vertically stretch by a factor of 3: g(x) = -3*x

and then shift down 1 unit: g(x) = -3*x -1

Option d

Shift right 1 unit: g(x) = x - 1

then reflect over the y-axis: g(x) = -x - 1

and then vertically stretch by a factor of 3: g(x) = -3*x - 1

Option e

Shift right 1 unit: g(x) = x - 1

then reflect over the x-axis: g(x) = -x + 1

and then vertically stretch by a factor of 3: g(x) = -3*x + 1

Option f

Shift down 1 unit: g(x) = x - 1

then reflect over the x-axis: g(x) = -x + 1

and then vertically stretch by a factor of 3: g(x) = -3*x + 1

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

answer is 144

step-by-step explanation: