I see the worksheet you've uploaded! Let's work through questions 5, 6, and 7.

Question 5:

In this question, you're given a graph, and you need to determine:

1. Domain (D): The set of all possible $x$-values.
2. Range (R): The set of all possible $y$-values.
3. If it is a function: A graph represents a function if each $x$-value corresponds to exactly one $y$-value (no vertical line crosses the graph more than once).

Analyzing the Graph in Question 5:

The graph looks like an upward-sloping curve.

• Domain: The $x$-values seem to extend infinitely in both directions, so the domain is all real numbers: $D = (-\infty, \infty)$
• Range: The curve seems to extend infinitely upward and downward, covering all possible $y$-values: $R = (-\infty, \infty)$
• Function: Since each vertical line only touches the curve at one point, it passes the vertical line test, so yes, it is a function.

Question 6:

This question provides a graph of a closed geometric shape, likely a polygon or curve.

Analyzing the Graph in Question 6:

• Domain: The graph appears to be a closed loop, suggesting a finite range of $x$-values. Let's assume the loop spans from $x = -3$ to $x = 3$: $D = [-3, 3]$
• Range: Similarly, the $y$-values range from $y = -3$ to $y = 3$, so: $R = [-3, 3]$
• Function: Since this graph does not pass the vertical line test (multiple $y$-values for a given $x$), it is not a function.

Question 7:

This graph shows a curve that appears to pass through multiple points, likely a continuous graph.

Analyzing the Graph in Question 7:

• Domain: The curve seems to extend infinitely left and right, so: $D = (-\infty, \infty)$
• Range: The curve likely extends infinitely upward and downward, covering all $y$-values: $R = (-\infty, \infty)$
• Function: The curve passes the vertical line test since no vertical line crosses the graph more than once, so it is a function.

Let me know if you need further clarifications or details.

Follow-up Questions:

1. Can you explain how to find the domain and range of a graph?
2. What is the vertical line test for a function?
3. How do we know if a function's domain is all real numbers?
4. What are some examples of graphs that are not functions?
5. How do we handle piecewise functions for domain and range?

Tip:

Always check the endpoints of a graph carefully to see if the domain and range are restricted or open-ended!