https://file.aiquickdraw.com/mathbot/file/1728661008153drih9lp5.jpg

https://file.aiquickdraw.com/mathbot/file/1728661008154tsx36mpz.jpg

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!

The original question submitted by the user as text.

Learn how to analyze functions and intercepts using a graph. This problem covers key math concepts such as identifying input and output quantities, finding intercepts, and evaluating functions. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation