Textbook Question
Determine whether each equation defines y as a function of x. y = √x +4
2. Graphs of Equations
Graphs and Coordinates
1:16 minutesProblem 33b
Textbook Question
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3 b. f(10)
Verified step by step guidance1
Step 1: Understand the problem. The function f(r) = √(r + 6) + 3 is given, and you are tasked with evaluating it at r = 10. This means substituting 10 for r in the function.
Step 2: Substitute r = 10 into the function. Replace r in the expression √(r + 6) + 3 with 10, resulting in f(10) = √(10 + 6) + 3.
Step 3: Simplify the expression inside the square root. Add 10 and 6 to get 16, so the function becomes f(10) = √(16) + 3.
Step 4: Evaluate the square root. The square root of 16 is 4, so the function simplifies further to f(10) = 4 + 3.
Step 5: Add the remaining terms. Combine 4 and 3 to complete the simplification of f(10).
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a specific value for the independent variable in a function. In this case, we replace 'r' in the function f(r) = √(r + 6) + 3 with the value 10. This process allows us to determine the output of the function for that particular input.
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Square Root Function
The square root function, denoted as √x, represents the principal square root of x, which is the non-negative value that, when squared, gives x. In the function f(r), the term √(r + 6) requires us to ensure that the expression inside the square root is non-negative, as square roots of negative numbers are not defined in the realm of real numbers.
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Simplification
Simplification is the process of reducing an expression to its simplest form. After evaluating the function at a specific value, we may need to combine like terms or perform arithmetic operations to arrive at a final, simplified answer. This step is crucial for clarity and ease of understanding in mathematical expressions.
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