Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 – 12 (5 points)

Describe how to transform the graph of f into the graph of g. (5 points) f(x) = and g(x) =

State the horizontal asymptote of the rational function. (5 points)f(x) =  

Where there are several layers of reinforcement, a continuous horizontal opening large enough for the concrete vibrator to pass through should be provided.

Find the exact value of the real number y. y = csc-1(1) (5 points)

A 124-mm-long beam supports a load of P = 48 N at midspan. The cross section is rectangular with width b = 25 mm and height h = 40 mm. Determine the magnitude of the horizontal shear stress at the centroid of the cross section.

Brittle materials fail due to maximum shear stress rather than principal stresses.

; g(x) = 8x – 7Find f(g(x)). (5 points)

Perform the requested operation or operations. f(x) = ; g(x) = 8x + 3, find g(f(x)). (5 points)

Compute φVn for the cross section shown. Assume f’c = 8,000 psi, fyt = 60,000 psi, b = 15 in., d = 23 in., and that there are four No. 6 longitudinal tension bars and No. 5 stirrups at 11 in. o.c.