8th grade math test on functions, Essays (high school) of Mathematics

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2023/2024

Uploaded on 04/08/2024

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8th Grade Math Practice Test: Functions
Name: _____________________________ Date: _________________
Instructions: Answer the following questions to the best of your ability. You may use a
calculator where necessary. Show all work for full credit.
1. What is a function? Explain in your own words and provide an example.
2. Consider the function f(x) = 3x + 4. What is the value of f(2)?
3. Write a function that models the relationship between the number of weeks (w) and the
number of hours (h) you spend practicing a musical instrument if you practice 5 hours each
week.
4. Graph the function g(x) = x^2 - 4x + 3. Label the x-axis, y-axis, and the vertex of the
parabola.
5. Compare the functions f(x) = 2x and g(x) = x^2. At what value of x do both functions have
the same value?
6. Given the function h(x) = 4x - 7, find the value of x when h(x) = 9.
7. The temperature (T), in degrees Celsius, as a function of the number of hours (h) after 6
a.m. is given by T(h) = -0.5h^2 + 4h + 10. What is the temperature at 10 a.m.?
8. Create a table of values for the function f(x) = -2x + 5 for x = -1, 0, 1, 2, 3.
9. How does changing the coefficient of x in a linear function f(x) = mx + b affect its graph?
Explain.
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8th Grade Math Practice Test: Functions

Name: _____________________________ Date: _________________ Instructions: Answer the following questions to the best of your ability. You may use a calculator where necessary. Show all work for full credit.

  1. What is a function? Explain in your own words and provide an example.
  2. Consider the function f(x) = 3x + 4. What is the value of f(2)?
  3. Write a function that models the relationship between the number of weeks (w) and the number of hours (h) you spend practicing a musical instrument if you practice 5 hours each week.
  4. Graph the function g(x) = x^2 - 4x + 3. Label the x-axis, y-axis, and the vertex of the parabola.
  5. Compare the functions f(x) = 2x and g(x) = x^2. At what value of x do both functions have the same value?
  6. Given the function h(x) = 4x - 7, find the value of x when h(x) = 9.
  7. The temperature (T), in degrees Celsius, as a function of the number of hours (h) after 6 a.m. is given by T(h) = -0.5h^2 + 4h + 10. What is the temperature at 10 a.m.?
  8. Create a table of values for the function f(x) = -2x + 5 for x = -1, 0, 1, 2, 3.
  9. How does changing the coefficient of x in a linear function f(x) = mx + b affect its graph? Explain.
  1. A store charges p dollars for buying q pounds of apples, where p = 1.5q + 0.5. How much does it cost to buy 4 pounds of apples?
  2. If f(x) = x^2 + x - 6 and g(x) = 2x - 3, find f(2) + g(2).
  3. The function f(x) = 1/2x - 3 models the relationship between x hours of tutoring and the improvement in a student’s test scores. What does the slope of this function represent?
  4. Explain the difference between a linear and a quadratic function using examples.
  5. If the function f(x) = 3x^2 - 12x + 11 represents the profit (f), in hundreds of dollars, of selling x items, how many items must be sold to achieve a profit of $800?
  6. Given two functions, f(x) = x^3 - 2x^2 + x - 1 and g(x) = x - 1, for which values of x is f(x) = g(x)?
  7. The function C(d) = 0.75d + 20 represents the cost (C), in dollars, of renting a car for d days. How much does it cost to rent the car for 7 days?
  8. Explain how the concept of a function can be used to model real-world relationships. Give two examples.
  9. A function f is defined as f(x) = 2^x. What is f(3)?
  10. If g(x) = |x - 2|, graph the function and describe its shape.
  11. The function V(r) = 4/3 πr^3 models the volume of a sphere with radius r. What is the volume of a sphere with a radius of 3 cm?