Find the remainder when f(x) is divided by (x – k). f(x) = 8×4 + 7×3 + 5×2 – 5x + 35; k = 4 (5 points)

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

Determine the intervals on which the function is increasing, decreasing, and constant. (5 points)

The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 30 + 0.006p3 and that its demand function is D(p) = 150 – 0.12p2, where p is the price. Determine the price for which the supply equals the demand. (5 points)

Verify the identity.sin = cos x (7 points) 

Write the expression as the sine, cosine, or tangent of an angle. sin 52° cos 13° – cos 52° sin 13° (6 points)

Verify the identity.   cos = -sin x (7 points) 

Verify the identity. cos (x – y) – cos (x + y) = 2 sin x sin y (5 points)

Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x + 14)2 (5 points)

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