To solve this problem, we need to determine which of the given graphs represent functions. A graph represents a function if it passes the
vertical line test: any vertical line drawn on the graph should intersect the curve at most once.
Let's analyze each graph:
1.
Graph 1: This is a parabola opening to the right. If we draw a vertical line, it will intersect the graph at two points for some x-values. Therefore, it does not represent a function.
2.
Graph 2: This is a sine wave. Any vertical line will intersect the graph at most once. Therefore, it represents a function.
3.
Graph 3: This is a circle. If we draw a vertical line, it will intersect the circle at two points for some x-values. Therefore, it does not represent a function.
4.
Graph 4: This is a straight line. Any vertical line will intersect the graph at most once. Therefore, it represents a function.
5.
Graph 5: This is an ellipse. If we draw a vertical line, it will intersect the ellipse at two points for some x-values. Therefore, it does not represent a function.
6.
Graph 6: This is a hyperbola. If we draw a vertical line, it will intersect the hyperbola at two points for some x-values. Therefore, it does not represent a function.
For part B, we need to determine which of the given graphs represents a function using the same vertical line test.
1.
Graph a: This is a cubic function. Any vertical line will intersect the graph at most once. Therefore, it represents a function.
2.
Graph b: This is a step function. Any vertical line will intersect the graph at most once. Therefore, it represents a function.
3.
Graph c: This is a sine wave. Any vertical line will intersect the graph at most once. Therefore, it represents a function.
Final Answer:
A)
1) No
2) Yes
3) No
4) Yes
5) No
6) No
B)
a) Yes
b) Yes
c) Yes
Parent Tip: Review the logic above to help your child master the concept of examples of relations and functions worksheet.
