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- Suppose the graph of f(x) = x3is compressedvertically using a factor of 1/3and then shifted to theleft 5 units. What is the equation of the new graph?Verify the result graphically.Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.Sketch one cycle of the graph of y=2sin(2x−π/3) At which x-values does the function take its maximum and minimum values on [0,π]
- State why the function 2z2 - 3z + e-z is analytic everywhere.Suppose (12,4) is a point on the graph of y=f(x). What is a point that will be on the graph of y=−6f(x)−1?Suppose the graph of f(x) = 1/xis stretched vertically by a factor of 4 and then shifted down 3 units.What is the equation of the new graph? Verify theresult graphically
- Suppose (x)= -4x. Determine and graph four distinct antiderivatives of f. Refer to image below of graph13. Find the minimum and maximum value of the function on the giveninterval.y = 2x 2 + 4x + 5 [-2, 2]Use the graph of y = f(x) to find the open intervals on which the graph of each transformation is increasing and decreasing. If not possible, state the reason.
- Show that the graph of f(x)=(3-4x)/e^2x has minimum value at x=5/4.Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y, then: Possible answers in the picturePresent a combinatorial argument to justify your answer. How many functions are there from {1, · · · , n} to {0, 1}?