Question

1. elena is ordering doughnuts for new members of her art club. depending on how many sign up, she will need to buy at least 3 and no more than 8 doughnuts. doughnuts are on sale for $2.00 each. the total cost, ( c(d) ), is a function of the number of doughnuts purchased, ( d ). describe the domain and range for this function. domain: range: 2. describe the domain and range for this function. domain: range: graph 3. to conduct an experiment, the room temperature in a lab needs to be as close as possible to 2 degrees celsius. any variation from this target temperature, whether warmer or cooler, is considered an error that could affect the experiment. let ( v ) be the function that gives the absolute temperature error for any given room temperature ( x ), in degrees celsius. graph re is the graph of a function. graph select all statements that are true about this function and this situation. a. the equation ( v(x) = |x - 2| ) gives the absolute temperature error when the room temperature is ( x ) degrees celsius. b. when ( v(x) = 0.5 ), the room temperature could be 1.5 or 2.5 degrees celsius. c. the equation ( v(x) = |x + 2| ) gives the absolute temperature error when the room temperature is ( x ) degrees celsius. d. when the room temperature is 0 degrees celsius, ( v(0) ) has a value of 2. e. when the room temperature is (-3) degrees celsius, the absolute temperature error is (-5). f. when the room temperature is 5 degrees celsius, ( v(5) ) is 3. multiple choice. which one of the equations below could represent this function? select one. a. ( f(x) = |x| - 1 ) b. ( g(x) = |x + 1| ) c. ( h(x) = |x - 1| ) d. ( j(x) = |x| + 1 )

Explanation:

Problem 1

Step1: Identify domain constraints

Elena buys 3 to 6 doughnuts, so $d \in \{3,4,5,6\}$.

Step2: Calculate cost for each $d$

Cost formula: $C(d) = 2.00d$

• $C(3)=2\times3=6$, $C(4)=2\times4=8$, $C(5)=2\times5=10$, $C(6)=2\times6=12$

Step1: Identify domain (x-values)

Graph uses integer x-values from 1 to 8.

Step2: Identify range (y-values)

Graph uses y-values from 3 to 9.

• a: Target temp is 2°C, error is $|x-2|$, so this is true.
• b: $v(x)=0.5$ means $|x-2|=0.5$, so $x=2.5$ or $1.5$, true.
• c: The formula is $|x-2|$, not $|x+2|$, false.
• d: $v(0)=|0-2|=2$, which is a valid value, true.
• e: Absolute error cannot be negative, false.
• f: $v(5)=|5-2|=3$, not 5, false.

Answer:

Domain: $\{3, 4, 5, 6\}$
Range: $\{6, 8, 10, 12\}$

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Problem 2