The profile of a mountain ridge is modeled by a cubic function y=M(x)y = M(x)y=M(x). The curve passes through the points (−4,0)(-4, 0)(−4,0) and (0,8)(0, 8)(0,8) and has a local minimum that touches the xxx-axis at the point (2,0)(2, 0)(2,0).
On separate diagrams, sketch the curve with equation:
y=M(x−4)y = M(x - 4)y=M(x−4)
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
y=M(−2x)y = M(-2x)y=M(−2x)
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
