Textbook Question
Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. 2 y = ——— x - 3
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0. Review of College Algebra
Functions
1:02 minutesProblem 53
Textbook Question
Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(p)
Verified step by step guidance1
Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
To find ƒ(p), substitute the variable x in the function ƒ(x) with p.
Write the expression after substitution: ƒ(p) = -3p + 4.
Simplify the expression if possible. In this case, the expression is already simplified.
The final expression for ƒ(p) is -3p + 4.
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Notation and Evaluation
Function notation, such as f(x), represents a rule that assigns each input x to an output f(x). Evaluating a function at a specific input, like f(p), means substituting the variable with the given value and simplifying the expression.
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i & j Notation
Polynomial Functions
Polynomial functions are expressions involving variables raised to whole number powers with coefficients. Understanding how to manipulate and simplify polynomials, such as linear (f(x) = -3x + 4) and quadratic (g(x) = -x² + 4x + 1), is essential for evaluating and combining functions.
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Substitution Method
The substitution method involves replacing the variable in a function with a given value or expression. This technique is crucial for finding function values like f(p), where p is substituted into the function's formula to compute the result.
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