Select the correct answer from each drop-down menu.
Laura and Becky are each graphing a transformation of the parent cosine function.
Laura’s function is a transformation where the parent function is horizontally compressed by a factor of
and is reflected over the x-axis.
Becky’s function is defined by the equation
f(x) = 3 cos (x - (pi))
Determine which graph belongs to each student.
Graph Student Answer
Graph shows a sinusoidal function plotted on coordinate plane with vertical axis f of x. A curve enters quadrant 2 at (minus 3pi by 2, 0), goes through (minus pi, 3), (minus pi by 2, 0), (0, minus 3), (pi by 2, 0) and exits quadrant 1 (3 pi by 2, 0). Graph shows a sinusoidal function plotted on coordinate plane with vertical axis f of x. A curve enters quadrant 3 at (minus 3pi by 2, 0), goes through (minus pi, minus 1), (minus pi by 2, 0), (0, 1), (pi by 2, 0) and exits quadrant 1 (3 pi by 2, 0). Graph shows sinusoidal function plotted on coordinate plane with vertical axis f of x. A curve enters quadrant 3 at (minus 3pi by 2, 0), goes through (minus pi, 1), (minus pi by 2, 0), (0, minus 1), (pi by 2, 0), and exits quadrant 1 (3 pi by 2, 0).
Laura: Graph shows sinusoidal function plotted on coordinate plane with vertical axis f of x. A curve enters quadrant 3 at (minus 3pi by 2, 0), goes through (minus pi, 1), (minus pi by 2, 0), (0, minus 1), (pi by 2, 0), and exits quadrant 1 (3 pi by 2, 0).
Becky: Graph shows a sinusoidal function plotted on coordinate plane with vertical axis f of x. A curve enters quadrant 2 at (minus 3pi by 2, 0), goes through (minus pi, 3), (minus pi by 2, 0), (0, minus 3), (pi by 2, 0) and exits quadrant 1 (3 pi by 2, 0).