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

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

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0:38 minutes

Problem 51

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(0)

Verified step by step guidance

Identify the function ƒ(x) given in the problem: ƒ(x) = -3x + 4.

To find ƒ(0), substitute x = 0 into the function ƒ(x).

Replace x with 0 in the expression: ƒ(0) = -3(0) + 4.

Simplify the expression by performing the multiplication: -3(0) = 0.

Add the results: 0 + 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 value into a function to determine its output. For example, to evaluate ƒ(0) for the function ƒ(x) = -3x + 4, you replace x with 0, resulting in ƒ(0) = -3(0) + 4 = 4. This process is fundamental in understanding how functions behave at particular points.

Linear Functions

A linear function is a polynomial function of degree one, which can be expressed in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. In the given function ƒ(x) = -3x + 4, the slope is -3, indicating a decrease in value as x increases, while the y-intercept is 4, showing where the line crosses the y-axis.

Simplification of Expressions

Simplification involves reducing mathematical expressions to their simplest form. This can include combining like terms, factoring, or reducing fractions. In the context of evaluating functions, simplification ensures that the final answer is presented in the most concise and understandable manner, which is essential for clarity in mathematical communication.