Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A landscaper is planning a circular garden. The cost C (in dollars) to plant the garden is a function of its radius r (in meters), given by C(r) = 5πr^2 + 10πr. What is the cost to plant a garden with a radius of 3 meters?
- A90π dollars
- B60π dollars
- C45π dollars
- D75π dollars
Show answer & explanationAnswer & explanation
Correct answer: D. 75π dollars
To find the cost, substitute r = 3 into the function C(r) = 5πr^2 + 10πr. C(3) = 5π(3)^2 + 10π(3) = 5π(9) + 30π = 45π + 30π = 75π.
Why the other options are wrong
- A. Incorrect. This would be if the radius was 4 for the second term, or another calculation error.
- B. Incorrect. This might be a calculation error, e.g., 5π(3)^2 + 10π(2).
- C. Incorrect. This would be 5πr^2 only, or an error in calculation.
Evaluating Functions
The process of substituting a given value for the independent variable into a function's expression to find the corresponding output value.
- Replace every instance of the variable.
- Follow order of operations (PEMDAS).
- The output is the function's value at that input.
Memory trick: Input is like a key, it unlocks the function's output door.