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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 65
Chapter 3, Problem 65

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(2m-3)

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Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
To find ƒ(2m - 3), substitute the expression (2m - 3) in place of x in the function ƒ(x).
Write the substitution explicitly: ƒ(2m - 3) = -3(2m - 3) + 4.
Apply the distributive property to multiply -3 by each term inside the parentheses: -3 \(\times\) 2m and -3 \(\times\) (-3).
Simplify the expression by combining like terms to get the final simplified form of ƒ(2m - 3).

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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. Evaluating a function means substituting the given expression or value into the function's formula and simplifying the result.
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Substitution of Algebraic Expressions

Substitution involves replacing the variable in a function with an algebraic expression, like 2m - 3, instead of a simple number. This requires careful algebraic manipulation to simplify the resulting expression correctly.
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Simplification of Algebraic Expressions

After substitution, simplifying the expression involves combining like terms and applying arithmetic operations to write the result in its simplest form. This step ensures the final answer is clear and concise.
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Related Practice
Textbook Question

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. through (9/4 , 2), undefined slope

Textbook Question

For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form. x - intercept (-3, 0), y-intercept (0, 5)

Textbook Question

For each line described, write an equation in

(a)slope-intercept form, if possible, and

(b)standard form.

through (0,5)(0, 5), perpendicular to 8x+5y=38x+5y=3

Textbook Question

Find and interpret the average rate of change illustrated in each graph.

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Textbook Question

Determine whether each function is even, odd, or neither. ƒ(x)=x4+4/x2

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Textbook Question

For each line described, write an equation in

(a)slope-intercept form, if possible, and

(b)standard form.

through (2,−10)(2, -10), perpendicular to a line with undefined slope.

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