Question

a1.4.09problems 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 onevalerias thiagos2. 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 neitherproblems 6-7 here is the graph of $g(r)$.6. write a compound inequality to describe the domain7. write a compound inequality to describe the range

Explanation:

Step1: Analyze domain of $f(x)$

The graph of $f(x)$ has endpoints at $x=-1.5$ and $x=2$, so these are the bounds of the domain.

Step2: Evaluate Valeria/Thiago's claim

Valeria states $-1.5 \leq x \leq 2$, which matches the graph's $x$-values. Thiago's values do not match the visible endpoints.

Step3: Identify domain of $d(t)$

Domain is the set of input ($t$, time) values. The graph spans $t=0$ to $t=2.1$.

Step4: Identify range of $d(t)$

Range is the set of output ($d(t)$, distance) values. The graph spans $d(t)=0$ to $d(t)=8$.

Step5: Analyze effect of skipping stop

Skipping the store would not change the total time to travel (domain) or the maximum distance from home (range).

Step6: Find domain of $g(r)$

The graph of $g(r)$ spans $r=0$ to $r=10$ on the horizontal axis.

Step7: Find range of $g(r)$

The graph of $g(r)$ spans $y=2$ to $y=8$ on the vertical axis.

Answer:

1. Valeria's
2. Thiago's answer uses $x$-values that do not match the actual endpoints of the $f(x)$ graph; the graph only exists between $x=-1.5$ and $x=2$.
3. C. $0 \leq t \leq 2.1$
4. B. $0 \leq d(t) \leq 8$
5. Neither
6. $0 \leq r \leq 10$
7. $2 \leq g(r) \leq 8$