In designing for shear, one must ensure that the shear strength equals or exceeds the flexural strength at all points in the beam.

The transformation from f to g represents a __________ stretch. (5 points) and Note: Use all lowercase letters in your response.

Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 + 9 (5 points)

Determine the function which corresponds to the given graph. (5 points) The asymptote is x = -5.

Find f(x) and g(x) so that the function can be described as y = f(g(x)). (5 points) y = + 9

Find the exact real value of arcsin . (5 points)

The decay of 923 mg of an isotope described by the function A(t)= 923e-0.027t, where t is time in years. Find the amount left after 76 years. Round your answer to the nearest mg. Show all of your work for full credit. (5 points)

Find the amplitude y = 3 sin x (5 points)

_______ must occur before a shear failure can occur in most concrete beams.

Find the zeros of the function. (5 points) f(x) = x2 – 6x + 8