Let the graph of f(x) represent the cost in thousands of dollars to feed the zoo animals daily, where x is the number of animals measured in hundreds. What does the solution to the function (2, 7) represent?
a graph of a function that decreases from the upper left, travels through an ordered pair labelled, 2, 7, and then increases toward the right
There are 200 animals, and the cost is $7,000 daily.
There are 2,000 animals, and the cost is $700 daily.
There are 700 animals, and the cost is $2,000 daily.
There are 7,000 animals, and the cost is $200 daily.
There are 200 animals, and the cost is $7,000 daily.
Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(150)?
f(150) represents the average number of days houses stay on the market before being sold for $150,000.
Houses sell on the market for an average of $150,000 and stay on the market an average of 150 days before being sold.
Houses sell for an average of $150,000.
f(150) indicates houses stay on the market an average of 150 days before being sold.
f(150) represents the average number of days houses stay on the market before being sold for $150,000.
If g(x) = x2 + 2, find g(3).
g(3) = 32 + 2 = 11
If g(x) = x2 + 2, find g(3).
9
8
11
6
g(3) = 32 + 2 = 11. Therefore, the correct answer is 11.
Jamie rents a movie for a flat fee of $2.50 plus an additional $0.75 for each night she keeps the movie. Choose the cost function that represents this scenario if x equals the number of nights Jamie has the movie.
c(x) = 2.50x + 1.25
c(x) = 3.25
c(x) = 2.50 + 0.75x
c(x) = (2.50 + 0.75)x
c(x) = 2.50 + 0.75x
For the function f(x) = x + 5, what is the ordered pair for the point on the graph where x = 4w?
(4w, x + 5)
(4w, 4w + 5)
(x, x + 5)
(x, 4w + 5)
(4w, 4w + 5)
If f(x) = 6(x − 2), find f(5).
18
36
108
216
f(5) = 6(5 − 2) = 18. Therefore, the correct answer is 18.
Use the graph to fill in the blank with the correct number.
f(−2) = ________
X, Y graph. Plotted points negative 3, 0, negative 2, 2, 0, 1, and 1, negative 2.
Numerical Answers Expected!
f(-2) = 2.
Janelle and her best friend Carmen go shopping. The function p(x) = 5x4 − 3x3 + 2x2 + 24 represents how much money each girl spent based on the number of hours they were shopping. If Janelle and Carmen each go shopping for 2 hours, how much money did they spend together?
$58
$62
$176
$124
When each girl went shopping for 2 hours, we have x = 2 for Janelle and Carmen. Therefore, Janelle spent p(2) = 5(2)^4 − 3(2)^3 + 2(2)^2 + 24 = 68 dollars, and Carmen also spent 68 dollars. Therefore, together they spent 68 + 68 = 136 dollars.
So, the answer is $136.
You are riding the bus to school, and you realize it is taking longer because of all the stops you are making. The time it takes to get to school, measured in minutes, is modeled using the function g(x) = x4 − 3x2 + 4x − 5, where x is the number of stops the bus makes. If the bus makes 2 stops after you board, how long does it take you to get to school?
1 minute
3 minutes
7 minutes
11 minutes
Answer this question seperately
Question 10(Multiple Choice Worth 1 points)
(02.02 MC)
Jade decided to rent movies for a movie marathon over the weekend. The function g(x) represents the amount of money spent in dollars, where x is the number of movies. Does a possible solution of (6.5, $17.50) make sense for this function? Explain your answer.
Yes. The input and output are both feasible.
No. The input is not feasible.
No. The output is not feasible.
No. Neither the input nor output is feasible.
When the bus makes 2 stops after you board, we have x = 2. Therefore, it takes g(2) = 2^4 − 3(2)^2 + 4(2) − 5 = 7 minutes to get to school.
So, the answer is 7 minutes.
For the second question, the answer is No. The input is not feasible. Since x represents the number of movies, it must be a whole number and cannot be 6.5. Therefore, (6.5, $17.50) does not make sense for this function.
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
1) To change the equation to slope-intercept form, we need to solve for y:
2x + 3y = 1470
3y = -2x + 1470
y = (-2/3)x + 490
Therefore, the equation in slope-intercept form is y = (-2/3)x + 490. The slope of the equation is -2/3, and the y-intercept is 490.
2) To graph this line using the slope-intercept method, we start at the y-intercept, which is (0, 490), and then use the slope to find another point on the line. Since the slope is -2/3, we can move down 2 units and to the right 3 units from the y-intercept to get to (3, 488). We can then draw a line through these two points to graph the equation.
3) The equation in function notation is f(x) = (-2/3)x + 490, where f(x) represents the profit from lunch specials in dollars and x represents the number of sandwich lunch specials sold. The graph of the function represents the relationship between the number of sandwich lunch specials sold and the profit from lunch specials in dollars.
4) Here is a hand-drawn graph of the function:
Graph of f(x) = (-2/3)x + 490
The x-intercept is found by setting y = 0:
0 = (-2/3)x + 490
(2/3)x = 490
x = 735
The y-intercept is (0, 490) and the x-intercept is (735, 0).
5) The graphs of the functions for the two months are similar because they have the same slope, which means that for every 3 wraps that Sal sells, he sells 2 sandwiches. However, the graphs are different because they have different y-intercepts, which represent the different profits that Sal made in the two months. Specifically, the y-intercept for the first month is $490, while the y-intercept for the second month is $531. This means that Sal made more profit in the second month than in the first month even though the profit amounts for each sandwich and wrap were the same.
write this smaller and with smaller words
The graphs of the functions for the two months are similar because they have the same slope, which means that for every 3 wraps that Sal sells, he sells 2 sandwiches. However, the graphs are different because they have different y-intercepts, which represent the different profits that Sal made in the two months. Specifically, the y-intercept for the first month is $490, while the y-intercept for the second month is $531. This means that Sal made more profit in the second month than in the first month even though the profit amounts for each sandwich and wrap were the same.