problems 1 - 2: valeria and thiago disagree about the domain of ( f(x) ).
valeria says the domain is ( -1.5 leq x leq 2 )
thiago says the domain is ( -4.375 leq x leq 3.5 )
1. whose answer is correct? circle one.
valerias thiagos
2. explain why the other persons answer is incorrect.
problems 3 - 5: haru bikes to his friends house. after a while, he heads home. on the way, he stops at the store to buy a bottle of water. ( d(t) ) represents harus distance from his house, in kilometers, after ( t ) hours. this graph shows harus distance over time.
3. which inequality describes the domain of ( d(t) )?
a. ( 0 leq d(t) leq 2.1 ) b. ( 0 leq d(t) leq 8 )
c. ( 0 leq t leq 2.1 ) d. ( 0 leq t leq 8 )
4. which inequality describes the range of ( d(t) )?
a. ( 0 leq d(t) leq 2.1 ) b. ( 0 leq d(t) leq 8 )
c. ( 0 leq t leq 2.1 ) d. ( 0 leq t leq 8 )
5. if haru had not stopped at the store, would that change the domain or the range? circle one.
domain range both neither
problems 6 - 7 here is the graph of ( g(r) ).
6. write a compound inequality to describe the domain.
7. write a compound inequality to describe the range.

Question

Accepted Answer

### Problem 1
# Explanation:
## Step1: Domain definition
The domain of a function is the set of all possible input values (x - values for $y = f(x)$). Looking at the graph, the left - most $x$ - value is $x=-1.5$ and the right - most $x$ - value is $x = 2$.
# Answer:
Valeria's

### Problem 2
# Brief Explanations:
Thiago likely confused the $x$ and $y$ values. The domain is about $x$ - values. The point $(-1.5,-4.375)$ has an $x=-1.5$ (domain value) and $y =-4.375$ (range value), and the point $(2,3.5)$ has $x = 2$ (domain value) and $y=3.5$ (range value). He might have taken the $y$ - values of the endpoints as part of the domain.
# Answer:
Thiago confused $x$ (domain) and $y$ (range) values.

### Problem 3
# Explanation:
## Step1: Domain concept
The domain of a function $y = d(t)$ is the set of all possible values of the independent variable. Here, the independent variable is $t$ (time). Looking at the graph of $d(t)$, the $t$ - values start at $t = 0$ and end at $t=2.1$.
# Answer:
C. $0\leq t\leq2.1$

### Problem 4
# Explanation:
## Step1: Range concept
The range of a function $y = d(t)$ is the set of all possible values of the dependent variable. Here, the dependent variable is $d(t)$ (distance). Looking at the graph of $d(t)$, the minimum value of $d(t)$ is $0$ (when $t = 2.1$) and the maximum value of $d(t)$ is $8$.
# Answer:
B. $0\leq d(t)\leq8$

### Problem 5
# Explanation:
## Step1: Domain and range analysis
The domain is related to time ($t$). If Haru does not stop at the store, the time ($t$) it takes him to go to his friend's house and come back home does not change. The range is related to the distance ($d(t)$). Since he still goes to his friend's house (maximum distance $d(t)=8$) and comes back home ($d(t) = 0$), the range does not change either.
# Answer:
Neither

### Problem 6
# Explanation:
## Step1: Identify domain endpoints
Looking at the graph of $g(r)$, the left - most $r$ - value is $r=-2$ and the right - most $r$ - value is $r = 15$.
# Answer:
$-2\leq r\leq15$

### Problem 7
# Explanation:
## Step1: Identify range endpoints
Looking at the graph of $g(r)$, the minimum $y$ - value (where $y = g(r)$) is $y=-2$ and the maximum $y$ - value is $y = 8$.
# Answer:
$-2\leq g(r)\leq8$

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QUESTION IMAGE

Question

Explanation:

Problem 1

Step1: Domain definition

Step1: Domain concept

Answer:

Problem 2