Consider the function f(x) = Ax + b, where A is a matrix with columns A1 and A2.

• In the figure, the point b and the vectors A1 and A2 are drawn. Find and label the points y = f(x) for these values of x: (m, n) for all values of m and n between -3 and +3.

• Find and shade in the image of the square with vertices x = (3, -1), (3, -2), (4, -2), (4, -1).

• Find and mark the points f(x) with x = (m, (1/2)m + 1), for integers m from -4 to +5.

For tell the points x which correspond to the points y = P, P1, P2.

• Suppose x = (x1, x2). What is true about the values of x1 and x2 if f(x) lies on the line PP2?

• Suppose x = (x1, x2). What is true about the values of x1 and x2 if f(x) lies on the line PP1?

For tell the points x which correspond to the points y = Q0, …, Q4. Also write each point as a combination x1A1 + x2A2 + b.

Write the vectors in the form m1A1 + m2A2 for each of the vectors in the left column.

Label the point P = b - A1 + 4A2 and draw an arrow representing v = - 2A1 + A2.

Plot and label the points Q(t) = P + tv, for integers t, for which the points Q lie inside the figure. Then also plot the points for all the values of t between these integers.