Let’s break down the questions in each image one by one.

First Image

The first image contains a set of problems related to a graph showing sales of blank cassette tapes over time. Let’s address each part:

1. Does the graph represent a function? Justify your answer.

   • Yes, the graph represents a function because for each value of the input (years since 1990), there is only one corresponding value for sales (in millions of dollars). This satisfies the definition of a function.

2. State the input and output quantities.

   • Input: Years since 1990.
   • Output: Sales in millions of dollars.

3. Interpret the meaning of the ordered pair (5, 30).

   • This ordered pair means that 5 years after 1990 (in 1995), the sales of blank cassette tapes were 30 million dollars.

4. State the meaning of $S(13) = 81$.

   • This means that 13 years after 1990 (in 2003), the sales were 81 million dollars.

5. Evaluate $S(18)$.

   • Based on the graph, we can approximate that $S(18)$ is about 260 million dollars.

6. Solve for $y$ when $S(y) = 120$ and state the meaning.

   • From the graph, we can estimate that $S(y) = 120$ occurs around year 15 (15 years after 1990, or 2005). This means that in 2005, the sales of blank cassette tapes were 120 million dollars.

Second Image

The second image presents a table and some questions about the function $c(p)$. Let’s go through them:

1. Vertical Intercept:

   • The vertical intercept is where the input $p = 0$. From the table, when $p = 0$, $c(0) = -2$. Thus, the vertical intercept is at $(0, -2)$.

2. Horizontal Intercept:

   • The horizontal intercept is where $c(p) = 0$. From the table, $c(p) = 0$ when $p = -1$, so the horizontal intercept is at $(-1, 0)$.

3. Evaluate $c(2)$:

   • From the table, $c(2) = 1$.

4. Solve $c(p) = -3$:

   • From the table, $c(p) = -3$ when $p = 1$. Therefore, $p = 1$.

Do you need further details or explanations for any part of these problems? Here are 5 related questions to explore further:

1. What is the difference between a function and a relation in mathematics?
2. How would you find the slope of a graph if given two points?
3. Can a vertical line ever represent a function? Why or why not?
4. How would you estimate values between points on a graph that doesn't show them explicitly?
5. What other types of intercepts exist, and how are they useful in graph analysis?

Tip: When analyzing graphs, it’s important to always check if each input has only one output, ensuring it meets the criteria for being a function!