Transformations: Write the equations of each of the following graphs b. The grap

Question

Transformations: Write the equations of each of the following graphs b. The graph of a function p(x) is shown Draw the graph of -p(x-2) + 3. c. Describe the transformations that have been applied to the graph of A(x) = Squareroot x to obtain the graph of a(x) = 2 Squareroot -x. Then, sketch the graph d Write the equation of the function that has a graph the shape of y = 3 Squareroot x. vertically shrunk by a factor of 1/4 and shifted right 6 units Then, sketch the graph Write the equation of the function that has a graph the shape of y = |x| reflected about the x-axis and shifted down 1 unit. Then, sketch the graph f. Describe the transformations that have been applied to the graph of F(x) = x^2 to obtain the graph of f(x) = x^2' to obtain the graph of f(x) = -(3x)^2 - 5.

Explanation / Answer

1a)

the first graph is transformation of |x|

|x| is shifted to 2 units to the right and 4 units downwards

therefore, function becomes

f(x) = | x - 2 | - 4

b) the 2nd graph is transformation of x^3

the function is reflected across y axis and shifted 1 unit upwards

therefore, function becomes

f(x) = -x^3+1

c) the 3rd function is transformation of sqrt x

the graph is reflected across x axis and shifted 4 units to the left

therefore, the function becomes

f(x) = - ( sqrt (x+4))

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