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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 34
Chapter 3, Problem 34

Let ƒ(x) = -2x2 + 3x -6. Find each of the following. ƒ(-0.5)

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1
Identify the given function: \(f(x) = -2x^2 + 3x - 6\).
Substitute the value \(x = -0.5\) into the function to find \(f(-0.5)\).
Calculate the square of \(-0.5\), which is \((-0.5)^2\).
Multiply the squared value by \(-2\), then multiply \(3\) by \(-0.5\), and finally subtract \(6\).
Add all the results together to get the value of \(f(-0.5)\).

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Key Concepts

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

Function Evaluation

Function evaluation involves substituting a given input value into the function's expression and simplifying to find the output. For example, to find ƒ(-0.5), replace every x in the function with -0.5 and calculate the result.
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Polynomial Functions

A polynomial function is an expression consisting of variables raised to whole-number exponents and coefficients. Understanding the structure of polynomials, like ƒ(x) = -2x² + 3x - 6, helps in correctly applying operations such as substitution and simplification.
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Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication/division, and addition/subtraction. Correctly applying this order ensures accurate evaluation of expressions like -2(-0.5)² + 3(-0.5) - 6.
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Related Practice
Textbook Question

Use the graph to evaluate each expression. See Example 3(a). 

(ƒ+g)(0)

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Textbook Question

Use the graph to evaluate each expression. See Example 3(a).

(ƒ/g)(1)

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Textbook Question

Use the graph to evaluate each expression. See Example 3(a).

(ƒg)(0)

1
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Textbook Question

Use the graph to evaluate each expression. See Example 3(a).

(ƒ-g)(-1)

Textbook Question

Use the graph to evaluate each expression. See Example 3(a).

(ƒg)(1)

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Textbook Question

Use the graph to evaluate each expression. See Example 3(a).

(ƒ-g)(1)

1
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