Based on my analysis of each graph using the vertical line test, here are the answers:
1) NOT a function - The curve opens to the right, so vertical lines intersect it at multiple points for some x-values.
2) IS a function - The wavy curve passes the vertical line test (each vertical line intersects at exactly one point).
3) IS a function - The parabola opening upward passes the vertical line test.
4) NOT a function - The sideways S-shaped curve has vertical lines that intersect it at multiple points.
5) IS a function - The straight line with negative slope passes the vertical line test.
6) NOT a function - The ellipse fails the vertical line test (vertical lines through the center intersect at two points).
7) IS a function - The hyperbola-like curve passes the vertical line test (each vertical line intersects at exactly one point in the visible portion).
8) IS a function - The piecewise graph passes the vertical line test (each vertical line intersects at exactly one point).
9) IS a function - The step function passes the vertical line test (each vertical line intersects at exactly one point).
The key principle used is the vertical line test: A graph represents a function if and only if every vertical line intersects the graph at most once. This ensures that for each input (x-value), there is exactly one output (y-value), which is the definition of a function.
Parent Tip: Review the logic above to help your child master the concept of features of functions worksheet answers.
