Graphical examples demonstrating the definitions of functions, one-to-one functions, and inverse functions using line tests.

Looking at the worksheet, I need to determine which graphs are functions and which are one-to-one functions.

First, let's recall what makes a graph a function:
- A graph is a function if every x-value has only one y-value.
- We use the vertical line test: if any vertical line crosses the graph more than once, it's NOT a function.

Now, for one-to-one functions:
- A function is one-to-one if every y-value corresponds to only one x-value.
- We use the horizontal line test: if any horizontal line crosses the graph more than once, it's NOT one-to-one.

Let me analyze each graph:

Section 1: Are these graphs functions?

Graph 1 (parabola opening up):
- If I draw vertical lines anywhere, they only cross the graph once.
- This IS a function.

Graph 2 (sideways parabola):
- If I draw a vertical line through the middle, it crosses the graph twice.
- This is NOT a function.

Graph 3 (straight line):
- Any vertical line crosses only once.
- This IS a function.

Section 2: Are these functions one-to-one?

Graph 1 (same parabola):
- If I draw a horizontal line above the vertex, it crosses twice.
- This is NOT one-to-one.

Graph 2 (cubic-like curve):
- Any horizontal line crosses only once.
- This IS one-to-one.

Graph 3 (straight line):
- Any horizontal line crosses only once.
- This IS one-to-one.

Final Answer:
Section 1: Graph 1 - Yes, Graph 2 - No, Graph 3 - Yes
Section 2: Graph 1 - No, Graph 2 - Yes, Graph 3 - Yes