Suppose f(x)=x^2 and g(x)=-1/5(x-3)^2. which statement best compares the graph of g(x) with the graph of f(x)? a. the graph of g(x) is the graph of f(x) compressed vertically, flipped over the x-axis, and shifted 3 units to the right. b. the graph of g(x) is the graph f(x) compressed vertically, flipped over the x-axis , and shifted 3 units to the left. c. the graph of g(x) is the graph of f(x) stretched vertically, flipped over the x-axis , and shifted 3 units to the left. d. the graph of g(x) is the graph of f(x) stretched vertically, flipped over the x-axis, and shifted 3 units to the right.

The correct option is A.

Step-by-step explanation:

The given functions are

It can be written as

        .... (1)          

The transformation is defined as

               .... (2)

Where, k is vertical stretch or compression, a is horizontal shift and b is vertical shift.

If |k|>1, then the graph stretch vertically and if 0<|k|<1, then graph compressed vertically.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From equation (1) and (2), we get

Here the negative means, the graph of f(x) flipped over the x-axis.

Since 0<|k|<1, therefore the graph compressed vertically.

The value of a is -3<0, so graph shifts 3 units right.

The graph of f(x) is the graph of g(x) compressed vertically, flipped over the x-axis, and shifted 3 units to the right.

Therefore the correct option is A.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

the anwser is d) 75°

step-by-step explanation: