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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 59
Chapter 3, Problem 59

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(p)

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1
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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to an output value. Evaluating a function at a specific input, like ƒ(p), means substituting the variable x with p and simplifying the expression to find the output.
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Polynomial Functions

Polynomial functions are expressions involving variables raised to whole-number exponents combined using addition, subtraction, and multiplication. Understanding the structure of linear (e.g., -3x + 4) and quadratic (e.g., -x² + 4x + 1) polynomials helps in evaluating and simplifying function expressions.
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Introduction to Polynomial Functions

Simplification of Algebraic Expressions

Simplification involves combining like terms and performing arithmetic operations to write expressions in their simplest form. After substituting values into functions, simplifying ensures the final answer is clear and concise, which is essential for accurate interpretation.
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Introduction to Algebraic Expressions
Related Practice
Textbook Question

Determine whether each function is even, odd, or neither. ƒ(x)=0.5x4-2x2+6

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Textbook Question

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. through (3, -4), m = - 1/3

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(k)

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Textbook Question

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. (g∘ƒ)(0)

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Textbook Question

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.

(ƒ∘g)(−2)(ƒ∘g)(-2)

Textbook Question

For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form. through (3, -5) with slope -2.