Business Calculus Quiz: Graph Interpretation
3 questions · exam conditions
0:00
Graph InterpretationQuestion 1 of 3

A demand function D(p)D(p) is graphed with price pp on the horizontal axis and quantity demanded on the vertical axis. The graph shows a y-intercept of 80, an x-intercept of 40, and the function is linear. If the company currently prices their product at $25, what is the slope of this demand function and what does it represent economically?

The slope is -2, indicating that for each $1 increase in price, demand decreases by 2 units on average
The slope is -2, representing the price elasticity of demand at the current price point of $25
The slope is -2, representing the marginal revenue loss per unit price increase at all price levels
The slope is -2, indicating the company's average profit margin decreases by $2 per unit in this price range
← Back to quizzes

Business Calculus Quiz

Business Calculus Quiz: Graph Interpretation

Practice Graph Interpretation in Business Calculus with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Graph Interpretation, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Calculus.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A demand function D(p)D(p) is graphed with price pp on the horizontal axis and quantity demanded on the vertical axis. The graph shows a y-intercept of 80, an x-intercept of 40, and the function is linear. If the company currently prices their product at $25, what is the slope of this demand function and what does it represent economically?

  1. The slope is -2, indicating that for each $1 increase in price, demand decreases by 2 units on average (correct answer)
  2. The slope is -2, representing the price elasticity of demand at the current price point of $25
  3. The slope is -2, representing the marginal revenue loss per unit price increase at all price levels
  4. The slope is -2, indicating the company's average profit margin decreases by $2 per unit in this price range
Explanation: With points (0, 80) and (40, 0), the slope is (0-80)/(40-0) = -2. This means for each $1 increase in price, quantity demanded decreases by 2 units. Choice B confuses slope with elasticity. Choice C incorrectly interprets slope as marginal revenue. Choice D incorrectly relates slope to profit margin.

Question 2

A company's profit function is graphed on a coordinate plane. The graph shows the function crosses the x-axis at x=2x = 2 and x=8x = 8, has a y-intercept of −24-24, and approaches negative infinity as xx approaches both positive and negative infinity. Based on this information, what can be concluded about the company's break-even points and long-term profitability?

  1. The company breaks even at 2 and 8 units, and will eventually become profitable in the long run due to economies of scale effects
  2. The company breaks even at 2 and 8 units, but will experience losses for very large production volumes (correct answer)
  3. The company has an initial loss of $24 at zero production and will always be profitable between 2 and 8 units of production
  4. The company loses $24 when producing zero units, but the end behavior indicates eventual profitability for large volumes
Explanation: The x-intercepts at x = 2 and x = 8 represent break-even points where profit = 0. The y-intercept of -24 means the company has a loss of $24 when producing zero units (perhaps due to fixed costs). The end behavior (approaching negative infinity as x approaches ±∞) indicates the company will experience losses for very large production volumes, contradicting the idea of long-term profitability through economies of scale.

Question 3

An investment value function shows the following characteristics: y-intercept at 1000, no x-intercepts in the visible domain, decreasing slope over time, and approaches a horizontal asymptote at y=3000y = 3000 as time approaches infinity. If the slope at t=2t = 2 years is 400 dollars per year, what does this information suggest about the investment's performance and risk profile?

  1. Initial investment of $1000 grows toward $3000 maximum value; the decreasing slope indicates diminishing returns but no risk of loss (correct answer)
  2. Initial value of $1000 appreciates with compound growth; the slope of 400 at t=2 represents the annual interest rate of 40%
  3. Starting investment of $1000 will triple in value; the decreasing slope shows increasing volatility and higher risk over time periods
  4. Principal investment of $1000 earns diminishing returns approaching $3000 limit; the decreasing slope indicates higher market risk
Explanation: The y-intercept of 1000 is the initial investment, the asymptote at 3000 represents the maximum value the investment approaches, and no x-intercepts means the value never reaches zero (no loss of principal). The decreasing slope indicates diminishing returns over time, but since the function never crosses the x-axis, there's no risk of losing the initial investment. Choice B incorrectly interprets the slope as an interest rate. Choices C and D incorrectly associate decreasing slope with increasing risk.