Textbook Question
Graph each function. Give the domain and range. g(x)=[[2x-1]]
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Ch. 2 - Graphs and Functions
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 3, Problem 56
Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(-7/3)
Verified step by step guidance1
Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
Substitute the value x = -\(\frac{7}{3}\) into the function ƒ(x). This means replacing every x in the expression with -\(\frac{7}{3}\).
Write the substitution explicitly: ƒ\(\left\)(-\(\frac{7}{3}\[\right\)) = -3 \(\times\) \(\left\)(-\(\frac{7}{3}\]\right\)) + 4.
Multiply -3 by -\(\frac{7}{3}\) carefully, remembering that multiplying two negatives results in a positive.
After the multiplication, add 4 to the result to simplify the expression and find ƒ\(\left\)(-\(\frac{7}{3}\)\(\right\)).
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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 formula and simplifying to find the output. For example, to find ƒ(-7/3), replace x with -7/3 in ƒ(x) and simplify the expression.
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Evaluating Composed Functions
Linear Functions
A linear function has the form ƒ(x) = mx + b, where m and b are constants. Its graph is a straight line, and evaluating it involves simple arithmetic operations like multiplication and addition.
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Simplifying Rational Expressions
When substituting fractions into functions, it's important to carefully perform arithmetic with rational numbers. Simplifying involves reducing fractions and combining terms to express the result in simplest form.
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05:07Simplifying Algebraic Expressions
Related Practice
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Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (4, 1), parallel to y=-5
Textbook Question
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=-|x+4|
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Textbook Question
For each line, (a) find the slope and (b) sketch the graph. 4x + 3y = 12
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Textbook Question
Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-2, -2), parallel to y=3
Textbook Question
For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.