8. A math teacher adopts the following function to curve her students' midterm grades: f(x) = 10√x where x is the original midterm grade and f(x) is the improved midterm grade after the curve function is applied. a. Find the curved grade if a student scored 64 on the midterm. b. Find the curved grade if a student scored 81 on the midterm. c. Provide an example of a student's midterm grade in which the function will fail to improve the grade.
8. A math teacher adopts the following function to curve her students' midterm grades: f(x) = 10√x where x is the original midterm grade and f(x) is the improved midterm grade after the curve function is applied. a. Find the curved grade if a student scored 64 on the midterm. b. Find the curved grade if a student scored 81 on the midterm. c. Provide an example of a student's midterm grade in which the function will fail to improve the grade.
Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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8.)
![8. A math teacher adopts the following function to curve her students' midterm grades:
\[ f(x) = 10 \sqrt{x} \]
where \( x \) is the original midterm grade and \( f(x) \) is the improved midterm grade after the curve function is applied.
a. Find the curved grade if a student scored 64 on the midterm.
b. Find the curved grade if a student scored 81 on the midterm.
c. Provide an example of a student's midterm grade in which the function will fail to improve the grade.
d. The following graph displays the curve function \( f(x) = 10 \sqrt{x} \) in red as well as the non-curve function \( g(x) = x \) in blue. Based on the graph, do you think this curve system is fair to all students? Why or why not?
**Graph Description:**
- The graph is plotted with two lines: a red curve representing \( f(x) = 10 \sqrt{x} \) and a blue line representing \( g(x) = x \).
- The x-axis and y-axis both range from 0 to 100, each increment marked by a 10-unit grid.
- The origin (0,0) and the point (100,100) are specifically labeled.
- The red curve starts at (0,0) and rises gradually, becoming steeper as it approaches (100,100), indicating the effect of the curve.
- The blue line is a straight diagonal from (0,0) to (100,100), representing the original grades without a curve.
The graph illustrates how the red curve elevates the grades, especially at the lower end of the scale, while converging with the blue line at the higher end.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f7b3938-790b-4169-a858-04369df79473%2Fc8852cf9-4901-437f-8541-14fb4a4e9ef8%2Fna0558_processed.png&w=3840&q=75)
Transcribed Image Text:8. A math teacher adopts the following function to curve her students' midterm grades:
\[ f(x) = 10 \sqrt{x} \]
where \( x \) is the original midterm grade and \( f(x) \) is the improved midterm grade after the curve function is applied.
a. Find the curved grade if a student scored 64 on the midterm.
b. Find the curved grade if a student scored 81 on the midterm.
c. Provide an example of a student's midterm grade in which the function will fail to improve the grade.
d. The following graph displays the curve function \( f(x) = 10 \sqrt{x} \) in red as well as the non-curve function \( g(x) = x \) in blue. Based on the graph, do you think this curve system is fair to all students? Why or why not?
**Graph Description:**
- The graph is plotted with two lines: a red curve representing \( f(x) = 10 \sqrt{x} \) and a blue line representing \( g(x) = x \).
- The x-axis and y-axis both range from 0 to 100, each increment marked by a 10-unit grid.
- The origin (0,0) and the point (100,100) are specifically labeled.
- The red curve starts at (0,0) and rises gradually, becoming steeper as it approaches (100,100), indicating the effect of the curve.
- The blue line is a straight diagonal from (0,0) to (100,100), representing the original grades without a curve.
The graph illustrates how the red curve elevates the grades, especially at the lower end of the scale, while converging with the blue line at the higher end.
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