Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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1:23 minutes

Problem 65

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. ƒ(2m-3)

Verified step by step guidance

Identify the function ƒ(x) which is given as ƒ(x) = -3x + 4.

Substitute the expression (2m-3) in place of x in the function ƒ(x). This means wherever you see x in the function, replace it with (2m-3).

Apply the substitution: ƒ(2m-3) = -3(2m-3) + 4.

Distribute the -3 inside the parentheses: -3(2m-3) = -6m + 9.

Combine the result of the distribution with the constant term in the function: -6m + 9 + 4.

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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 specific input value into a function to determine its output. For example, if you have a function f(x) and you want to find f(a), you replace x with a in the function's expression. This process is essential for solving problems that require finding the value of a function at a given point.

Linear Functions

A linear function is a polynomial function of degree one, typically expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. In the given function f(x) = -3x + 4, the slope is -3, indicating a decrease in value as x increases. Understanding linear functions is crucial for analyzing their behavior and graphing them.

Substitution in Functions

Substitution in functions refers to replacing a variable in a function with another expression or value. In this case, substituting 2m - 3 into f(x) means calculating f(2m - 3) by replacing x in the function's formula with the expression 2m - 3. This technique is fundamental in algebra for manipulating and simplifying expressions.