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

Previous problemNext problem

1:20 minutes

Problem 66

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(3t-2)

Verified step by step guidance

Identify the function ƒ(x) = -3x + 4.

Substitute x with (3t - 2) in the function ƒ(x).

Write the expression: ƒ(3t - 2) = -3(3t - 2) + 4.

Distribute -3 across the terms inside the parentheses: -3 * 3t and -3 * (-2).

Simplify the expression by combining like terms.

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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. In this case, we need to evaluate the function ƒ(x) at the input (3t - 2). This process requires replacing every instance of 'x' in the function's expression with the given input.

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. The function ƒ(x) = -3x + 4 is linear, indicating that its graph is a straight line. Understanding the properties of linear functions is essential for evaluating and simplifying expressions involving them.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form, making it easier to understand or compute. After substituting (3t - 2) into the function ƒ(x), we will perform algebraic operations to simplify the resulting expression. This may include combining like terms and applying the distributive property.