VIPSolutionsGive step-by-step solution with explanation and final answer:ani anetion Notion row a Graph a Sew etn (1) reprenants Diyos distance from home after t hours. | [ 1, ai 110 El evaluate Hie fuetion at each value. Explain what ench bl means i terms of the problem | | (L] - | | \ a(n) = (7) ran Xi hd(s) = 2. 4.d(13) freee 2, Caloulits the visluo of that makes each equation true, Explain what cnch means in trms the problent adr) =a bod(t)=0 Part 51 Interpreting and Using Punction Notation: Smart Phones (4 ears after year 2000.
Question:
Give step-by-step solution with explanation and final answer:
ani anetion Notion row a Graph a Sew
etn (1) reprenants Diyos distance from home after t hours. | [
1, ai 110 El evaluate Hie fuetion at each value. Explain what ench bl
means i terms of the problem | | (L]
- | | \
a(n) = (7) ran Xi
hd(s) = 2. 4.d(13) freee
2, Caloulits the visluo of that makes each equation true, Explain what cnch means in trms the problent
adr) =a
bod(t)=0
Part 51 Interpreting and Using Punction Notation: Smart Phones
(4 ears after year 2000.
This is AI generated Response.
Asked by: anil
Created at: 2025-09-28 10:08:11
Asked by: anil
Created at: 2025-09-28 10:08:11
Final Answer:
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Let's solve each part step by step using the provided graph and explanations.
---
## **Given:**
- \( d(t) \) represents Diego's distance from home (in miles) after \( t \) hours.
---
### **1. Use the graph to evaluate the function at each value. Explain what each means in terms of the problem.**
#### **a. \( d(1) \)**
- **Find on the graph:** At \( t = 1 \), the graph shows \( d(1) = 1 \).
- **Explanation:** After 1 hour, Diego is **1 mile** from home.
#### **b. \( d(5) \)**
- **Find on the graph:** At \( t = 5 \), the graph shows \( d(5) = 2 \).
- **Explanation:** After 5 hours, Diego is **2 miles** from home.
#### **c. \( d(7) \)**
- **Find on the graph:** At \( t = 7 \), the graph shows \( d(7) = 6 \).
- **Explanation:** After 7 hours, Diego is **6 miles** from home.
#### **d. \( d(13) \)**
- **Find on the graph:** At \( t = 13 \), the graph shows \( d(13) = \).
- **Explanation:** After 13 hours, Diego is **back home** ( miles from home).
---
### **2. Calculate the value of \( t \) that makes each equation true. Explain what each means in terms of the problem.**
#### **a. \( d(t) = 4 \)**
- **Find \( t \) on the graph where \( d(t) = 4 \):** The graph shows \( d(t) = 4 \) at \( t = 8 \) and \( t = 10 \).
- **Answer:** \( t = 8 \) and \( t = 10 \).
- **Explanation:** Diego is **4 miles from home** at **8 hours** and again at **10 hours**.
#### **b. \( d(t) = \)**
- **Find \( t \) on the graph where \( d(t) = \):** The graph shows \( d(t) = \) at \( t = \) and \( t = 13 \).
- **Answer:** \( t = \) and \( t = 13 \).
- **Explanation:** Diego is **at home** at the **start ( hours)** and **after 13 hours**.
---
## **Summary Table**
| Part | Value from graph | Meaning in problem |
|-----------|-------------------------|--------------------------------------------|
| 1a | \( d(1) = 1 \) | 1 mile from home after 1 hour |
| 1b | \( d(5) = 2 \) | 2 miles from home after 5 hours |
| 1c | \( d(7) = 6 \) | 6 miles from home after 7 hours |
| 1d | \( d(13) = \) | Back home after 13 hours |
| 2a | \( t = 8, 10 \) | 4 miles from home at 8 and 10 hours |
| 2b | \( t = , 13 \) | At home at start and after 13 hours |
---
### **Final Answers**
1. a) \( d(1) = 1 \): 1 mile from home after 1 hour
b) \( d(5) = 2 \): 2 miles from home after 5 hours
c) \( d(7) = 6 \): 6 miles from home after 7 hours
d) \( d(13) = \): Home after 13 hours
2. a) \( t = 8, 10 \): 4 miles from home at 8 and 10 hours
b) \( t = , 13 \): At home at start and after 13 hours
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