The function y = 4x + 3 describes Player A's scores in a game of trivia, where x is the number of questions answered correctly and y is the score. The function represented in the t... The function y = 4x + 3 describes Player A's scores in a game of trivia, where x is the number of questions answered correctly and y is the score. The function represented in the table shows Player B's scores. What do the rates of change tell you about how each player earns points?
Understand the Problem
The question is asking for an analysis of the rates of change between the scores of two players in a trivia game, using a given mathematical function and a table of scores for Player B. The goal is to compare how each player earns points based on their performance.
Answer
Player A earns $4$ points per correct answer, while Player B earns $1$ point per correct answer.
Answer for screen readers
Player A earns points at a rate of 4 points per correct answer, while Player B earns only 1 point per correct answer.
Steps to Solve
- Define Player A's Function
Player A's score can be modeled by the function $y = 4x + 3$, where $x$ is the number of questions answered correctly. This means for each correct answer, Player A earns 4 points, plus a base of 3 points.
- Calculate Player A's Scores
Using the function, we will calculate Player A's score for different values of $x$:
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For $x = 1$: $$ y = 4(1) + 3 = 7 $$
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For $x = 2$: $$ y = 4(2) + 3 = 11 $$
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For $x = 3$: $$ y = 4(3) + 3 = 15 $$
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For $x = 4$: $$ y = 4(4) + 3 = 19 $$
- Analyze Player B's Scores
From the table provided for Player B, we note the scores corresponding to the number of correct answers:
- For 1 correct answer, score is 4
- For 2 correct answers, score is 5
- For 3 correct answers, score is 6
- For 4 correct answers, score is 7
- Calculate Rates of Change
Now, we will assess the rate of change for both players by examining the change in scores per correct answer.
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Player A: The increase in score per correct answer is consistently 4 points (scored calculated above).
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Player B: The scores increase as follows:
- From 1 to 2 answers: $5 - 4 = 1$
- From 2 to 3 answers: $6 - 5 = 1$
- From 3 to 4 answers: $7 - 6 = 1$
The rate of change for Player B is consistently 1 point per correct answer.
- Conclusion on Rates of Change
Player A earns 4 points for each correct answer, while Player B only earns 1 point per correct answer, indicating that Player A earns points at a much faster rate than Player B.
Player A earns points at a rate of 4 points per correct answer, while Player B earns only 1 point per correct answer.
More Information
This analysis shows that Player A has a much more effective scoring strategy compared to Player B, earning more points for each correct answer.
Tips
- Not associating correct answers with scores: It's crucial to match the number of correct answers with the corresponding score accurately.
- Failing to calculate correctly for Player A: Ensure to substitute values correctly into the function.
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