3. Functions

The graphs of two functions ƒ and g are shown in the figures.

Find (g∘ƒ)(3).

Fill in the blank to correctly complete each sentence.The point (-1, 3) lies in quadrant ________ in the rectangular coordinate system.

Fill in the blank to correctly complete each sentence.The point (4,_____ ) lies on the graph of the equation y = 3x - 6.

Fill in the blank to correctly complete each sentence.The y-intercept of the graph of y = -2x + 6 is ________.

Determine whether each statement is true or false. If false, explain why.The graph of y = x^2 + 2 has no x-intercepts.

Determine whether each statement is true or false. If false, explain why.The midpoint of the segment joining (0, 0) and (4, 4) is 2.

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. See Examples 2 and 5(a). P(-5,-6), Q(7,-1)

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. See Examples 2 and 5(a). P(8,2), Q(3,5)

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. See Examples 2 and 5(a). P(6,-2), Q(4,6)

Determine whether the three points are the vertices of a right triangle. See Example 3. (-2,-8),(0,-4),(-4,-7)

Determine whether the three points are the vertices of a right triangle. See Example 3. (-4,1),(1,4),(-6,-1)

Determine whether the three points are the vertices of a right triangle. See Example 3. (-2,-5),(1,7),(3,15)

Determine whether the three points are collinear. See Example 4. (0,-7),(-3,5),(2,-15)

Determine whether the three points are collinear. See Example 4. (0,9),(-3,-7),(2,-19)

Determine whether the three points are collinear. See Example 4. (-7,4),(6,-2),(-1,1)