Dependent Variables in Advanced Algebra
Explore the concept of dependent variables in advanced algebraic functions, including their identification, interpretation, and application in various mathematical contexts.
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Dependent Variables in Advanced Algebra
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Read each question carefully and provide clear, concise answers. Show all your work for problems requiring calculations.
1. In the function f(x) = 3x^2 - 5x + 2, which variable represents the dependent variable?
x
f(x)
3
2
2. If the cost C of producing x units of a product is given by C(x) = 100 + 5x, what is the dependent variable?
x
C(x)
100
5
3. In a functional relationship, the dependent variable's value the independent variable's value.
4. The output of a function is always the variable.
5. Consider the equation y = 2x - 7. Identify the dependent variable and explain why it is considered dependent.
6. In the equation A = πr^2, where A is the area of a circle and r is its radius, r is the dependent variable.
True
False
Match the scenario with its dependent variable.
7. The amount of gas remaining in a car's tank as a function of distance driven.
a. Distance driven
8. The height of a ball thrown upwards as a function of time.
b. Amount of gas remaining
9. The total cost of groceries based on the number of items purchased.
c. Height of the ball
10. The temperature of a room as the thermostat setting changes.
d. Total cost of groceries
e. Temperature of the room
11. A scientist is studying the growth of a plant. She measures the plant's height (h) in centimeters each week (w). Write a functional relationship that represents this scenario, clearly identifying the independent and dependent variables.
12. Plot the points (1, 3), (2, 5), (3, 7) on the coordinate plane below. Assume the x-axis represents the independent variable and the y-axis represents the dependent variable.