In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-2x-4) + 2.

Shift 2 unit left

Flip the graph about y-axis

Stretch horizontally by factor 2

Shift vertically up by 2 units

Step-by-step explanation:

Given:

Parent function:

Transformation function:

Take -2 common from transform function f(x)

Now we see the step-by-step translation

Shift 2 unit left ( x → x+2 )

Flip the graph about y-axis ( (x+2)  → - (x+2) )

Stretch horizontally by factor 2 [ -x(x+2) → -2(x+2) ]

Shift vertically up by 2 units [ f(x) → f(x) + 2 ]

Simplify the function:

Hence, Using four step of transformation to get new function

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

.

step-by-step explanation: