Question

match each graph with its ( x )-intercepts.

a. ( (-3,0),(0,0) )
b. ( (0,-3),(0,-2),(0,1),(0,0) )
c. ( (0,0),(0,2),(0,3) )
d. ( (0,0),(0,-3) )
e. ( (0,0),(1,0),(-2,0),(-3,0) )
f. ( (2,0),(0,0),(3,0) )
question help: video written example

Explanation:

First Graph (Top)

Step1: Identify x - intercepts

The x - intercepts are the points where the graph crosses the x - axis (where \(y = 0\)). Looking at the top graph, it crosses the x - axis at \(x = 0\), \(x=2\), and \(x = 3\). So the x - intercepts are \((0,0)\), \((2,0)\), and \((3,0)\).

Step2: Match with options

Among the given options, option f is \((2,0),(0,0),(3,0)\) which matches the x - intercepts of the top graph.

Second Graph (Middle)

Step1: Identify x - intercepts

The middle graph crosses the x - axis at \(x=-3\), \(x = - 2\), \(x=0\), and \(x = 1\). So the x - intercepts are \((-3,0)\), \((-2,0)\), \((0,0)\), and \((1,0)\).

Step2: Match with options

Among the given options, option e is \((0,0),(1,0),(-2,0),(-3,0)\) which matches the x - intercepts of the middle graph.

Third Graph (Bottom)

Step1: Identify x - intercepts

The bottom graph crosses the x - axis at \(x=-3\) and \(x = 0\). So the x - intercepts are \((-3,0)\) and \((0,0)\).

Step2: Match with options

Among the given options, option a is \((-3,0),(0,0)\) which matches the x - intercepts of the bottom graph.

Answer:

Top Graph: f. \((2,0),(0,0),(3,0)\)
Middle Graph: e. \((0,0),(1,0),(-2,0),(-3,0)\)
Bottom Graph: a. \((-3,0),(0,0)\)