Exercise 129 Page 251

a The domain and range of a graph shows which x- and y-values it can take. From the diagram, we notice that the graph is a continuous curve from x =-4 to x=3. Additionally, the point at x=-4 is filled while the point at x=3 is open. This means x=-4 is a part of the domain while x=3 is not. We show this with a solid and dashed line respectively.

Now we can write our domain.

Domain: -4 ≤ x < 3 Similarly, in the vertical direction, the graph is drawn between y=-5 and y=5 including the endpoints. We include them since (-3,5) and (0,-5) are both filled points.

Now we can write our range. Range: -5 ≤ y ≤ 5 This graph is a function because there is no point where one x-values gives multiple y-values.

b To draw the inverse, we will switch positions of the points x- and y-coordinates that fall on f(x).

|c|c| f(x) & f^(-1)(x) (-4,2) & (2,-4) (-3,5) & (5,-3) (0,-5) & (-5,0) (3,-1) & (-1,3)

Now we can graph the inverse.

A graph is only a function if it passes the vertical line test. This means any arbitrary vertical line can only intersect the graph once.

Since the vertical line intersects the graph twice, it is not a function.

c Just like we swap the x- and y-coordinates of points on the function to find points on the inverse, we can find the inverse domain and range by swapping the domain and range of the function.

Domain: -5 ≤ x ≤ 5 Range: -4 ≤ y < 3

Subchapter links

Exercises

126

127

128

129

130

131

132

133

134

Exercise 129 Page 251

Hints

Check the answer