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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0:52 minutes

Problem 52

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(-3)

Verified step by step guidance

Identify the function ƒ(x) = -3x + 4.

Substitute x = -3 into the function ƒ(x).

Calculate ƒ(-3) by replacing x with -3 in the expression: ƒ(-3) = -3(-3) + 4.

Simplify the expression by performing the multiplication: -3(-3).

Add the result of the multiplication to 4 to complete the simplification.

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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, to evaluate ƒ(x) at x = -3, you replace x in the function ƒ(x) = -3x + 4 with -3, resulting in ƒ(-3) = -3(-3) + 4.

Linear Functions

A linear function is a polynomial function of degree one, represented in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. In this case, ƒ(x) = -3x + 4 is a linear function with a slope of -3 and a y-intercept of 4, indicating a straight line when graphed.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form by combining like terms and performing arithmetic operations. In the context of evaluating functions, after substituting the input value, you may need to simplify the resulting expression to present the final answer clearly.