Modeling with Functions Practice Questions
Common Core (US) · Common Core Algebra 2 · 148 free MCQs with instant results and detailed explanations.
148
Total
55
Easy
71
Medium
22
Hard
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Sample Questions from Modeling with Functions
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
A linear function models the cost of producing x units of a product. If the cost function is C(x) = 50x + 200, what is the cost of producing 10 units?
A.
$700
B.
$500
C.
$600
D.
$800
Show Answer & Explanation
Correct Answer: A
To calculate the cost of producing 10 units, substitute x = 10 into the cost function: C(10) = 50(10) + 200 = 500 + 200 = 700.
Q2
Easy
A quadratic function is given by f(x) = x^2 - 4x + 3. What is the vertex of this parabola?
A.
(2, -1)
B.
(2, 1)
C.
(1, 2)
D.
(3, 0)
Show Answer & Explanation
Correct Answer: B
The vertex of a quadratic function in standard form ax^2 + bx + c can be found using the formula x = -b/(2a). Here, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Now substitute x = 2 back into the function to find f(2) = 2^2 - 4(2) + 3 = 1, giving the vertex (2, 1).
Q3
Easy
A company found that its revenue, R(x), in dollars from selling x items is modeled by the function R(x) = 20x. How much revenue does the company generate by selling 15 items?
A.
$300
B.
$400
C.
$250
D.
$350
Show Answer & Explanation
Correct Answer: A
To find the revenue from selling 15 items, substitute x = 15 into the revenue function: R(15) = 20(15) = 300. Thus, the revenue generated is $300.
Q4
Medium
A company finds that their profit P (in thousands of dollars) can be modeled by the function P(x) = -2x^2 + 12x - 10, where x is the number of units sold (in hundreds). What is the maximum profit the company can achieve?
A.
6 thousand dollars
B.
12 thousand dollars
C.
18 thousand dollars
D.
24 thousand dollars
Show Answer & Explanation
Correct Answer: B
The maximum profit occurs at the vertex of the parabola, given by x = -b/(2a). Here, a = -2 and b = 12, so x = 12/(2*2) = 3 (hundreds). Plugging x = 3 into the profit function gives P(3) = -2(3^2) + 12(3) - 10 = 12. Thus, the maximum profit is 12 thousand dollars.
Q5
Medium
A quadratic function is modeled by the equation f(x) = -2x^2 + 4x + 1. What is the maximum value of f(x)?
A.
5
B.
7
C.
3
D.
4
Show Answer & Explanation
Correct Answer: A
The maximum value of a quadratic function in the form f(x) = ax^2 + bx + c occurs at x = -b/(2a). Here, a = -2 and b = 4. Thus, x = -4/(2*(-2)) = 1. Substituting x = 1 into the function gives f(1) = -2(1)^2 + 4(1) + 1 = 5.
Q6
Medium
A linear function is modeled by the equation y = 3x + 2. If this function represents a cost in dollars for x items sold, what is the cost for selling 10 items?
A.
32
B.
30
C.
35
D.
28
Show Answer & Explanation
Correct Answer: A
To find the cost of selling 10 items, substitute x = 10 into the function: y = 3(10) + 2 = 30 + 2 = 32. Thus, the total cost for selling 10 items is $32.
Q7
Medium
A researcher models the relationship between hours studied (x) and test scores (y) with the function y = 15x + 50. What test score corresponds to studying for 4 hours?
A.
110
B.
100
C.
80
D.
90
Show Answer & Explanation
Correct Answer: A
To find the score for 4 hours of study, substitute x = 4 into the equation: y = 15(4) + 50 = 60 + 50 = 110. Therefore, studying for 4 hours corresponds to a score of 110.
Q8
Hard
A population of bacteria grows according to the function P(t) = 100e^(0.3t), where P is the population at time t in hours. How long will it take for the population to exceed 1000?
A.
5 hours
B.
7.5 hours
C.
10 hours
D.
12 hours
Show Answer & Explanation
Correct Answer: B
To find when the population exceeds 1000, we set 100e^(0.3t) > 1000. Dividing both sides by 100 gives e^(0.3t) > 10. Taking the natural logarithm of both sides yields 0.3t > ln(10). Solving for t gives t > ln(10)/0.3, which approximates to 7.5 hours.
Q9
Hard
A company's profit, P, in thousands of dollars, can be modeled by the function P(x) = -2x^2 + 12x - 10, where x represents the number of units sold in thousands. How many units must be sold to maximize profit?
A.
3,000 units
B.
2,000 units
C.
6,000 units
D.
4,000 units
Show Answer & Explanation
Correct Answer: A
To maximize profit, we need to find the vertex of the parabola given by the quadratic equation. The x-coordinate of the vertex is found using x = -b/(2a). Here, a = -2 and b = 12, so x = -12/(2 * -2) = 3. Thus, 3,000 units must be sold to maximize profit.
Q10
Hard
A car rental company charges a base fee of $30 per day plus an additional charge of $0.20 per mile driven. If a customer rents a car for a day and drives a total of 150 miles, what will be the total cost of the rental?
A.
$60
B.
$75
C.
$90
D.
$105
Show Answer & Explanation
Correct Answer: C
The total cost, C, can be calculated using the formula C = base fee + (cost per mile * miles driven). Here, C = 30 + (0.20 * 150) = 30 + 30 = 90. Therefore, the total cost is $90.
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Modeling with Functions — Common Core (US) Common Core Algebra 2 Practice Questions Online
This page contains 148 practice MCQs for the chapter Modeling with Functions in Common Core (US) Common Core Algebra 2. The questions are organized by difficulty — 55 easy, 71 medium, 22 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.