To analyze and solve the questions on this worksheet, I will go through each graph and determine whether it represents a function, along with identifying its domain, range, and x- and y-intercepts.

Analysis of Each Graph

1. Graph 7

   • Function: Yes, this is a function because it passes the vertical line test.
   • Domain: All real numbers (typically written as $x \in (-\infty, \infty)$)
   • Range: All real numbers (typically $y \in (-\infty, \infty)$, assuming the curve does not restrict values)
   • X-intercept: The point where the curve crosses the x-axis.
   • Y-intercept: The point where the curve crosses the y-axis.

2. Graph 8

   • Function: Yes, this is a function.
   • Domain: All real numbers $x \in (-\infty, \infty)$
   • Range: It appears that the range is limited by the vertical stretch of the curve.
   • X-intercept: Where the curve crosses the x-axis.
   • Y-intercept: The point where the curve crosses the y-axis.

3. Graph 9

   • Function: No, this is not a function as it fails the vertical line test (due to the circular shape).
   • Domain: Limited to the x-values within the circle's width.
   • Range: Limited to the y-values within the circle's height.
   • X-intercept: Points where the circle intersects the x-axis.
   • Y-intercept: Points where the circle intersects the y-axis.

4. Graph 10

   • Function: Yes, this is a function.
   • Domain: All real numbers $x \in (-\infty, \infty)$
   • Range: Determined by the highest and lowest points of the oscillating curve.
   • X-intercept: Points where the wave crosses the x-axis.
   • Y-intercept: The point where the wave crosses the y-axis.

Each of these questions requires calculating or estimating intercepts and determining the exact domain and range based on the graph's visual characteristics.

Would you like further details or have any specific questions?

Here are some related questions that might help deepen your understanding:

1. How do you determine the domain and range of a function just by looking at a graph?
2. What does it mean for a graph to pass or fail the vertical line test?
3. Why does a circle not represent a function?
4. How can intercepts be used to understand the behavior of a function?
5. What are common domain and range restrictions for different types of functions?

Tip: Always use the vertical line test to quickly check if a graph represents a function by seeing if any vertical line crosses the graph more than once.