Sketch a SINGLE graph that includes all of the conditions below. • f'(x) > 0 when - 4< x < 1 f'(x) < 0 when x < -4 and when x > 1 - 5 f(-4) f(1) = 5

The graph of y = f(x) is transformed by a horizontal expansion by a factor of 4 and a vertical expansion by a factor of 5. The equation of this new image has the form y = af(bx); find a and b. O a a = 5, 6 = }, 6 = | O a = b = 4 O a = O a = 5, b = 4

Find the point on the graph of the function y = 4 - x2 that is closest to the point (0,2)

Graph y = 5e-xon [-4, 4] by [-1, 20] .

The graph of a function f is shown below in green, along with a transformation of f shown in black. Use transformations (shifting and/or reflecting only) to express Graph I in terms of f (x). Example: if f is shifted down 2 units, then you would enter f (x) – 2

Find g(1) if g(x)=x^2+1

Is the graph of g(x)=4x^3+9x^2+7x+3 concave up or down at the point with x-coordinate −2?