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

Transformations

College Algebra

3. Functions

Transformations

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1:13 minutes

Problem 99

Textbook Question

Let ƒ(x) = 3x -4. Find an equation for each reflection of the graph of ƒ(x).across the y-axis

Verified step by step guidance

Identify the transformation needed: Reflecting a function across the y-axis involves changing the sign of the x-variable in the function.

Start with the original function: \( f(x) = 3x - 4 \).

To reflect across the y-axis, replace \( x \) with \( -x \) in the function.

Substitute \( -x \) into the function: \( f(-x) = 3(-x) - 4 \).

Simplify the expression: \( f(-x) = -3x - 4 \). This is the equation of the reflection of the graph of \( f(x) \) across the y-axis.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Reflection Across the Y-Axis

Reflecting a graph across the y-axis involves transforming the function by replacing x with -x. For a function ƒ(x), the reflection is represented as ƒ(-x). This changes the sign of the x-coordinates of all points on the graph, effectively flipping it over the y-axis.

Linear Functions

A linear function is a polynomial function of degree one, typically expressed in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line, and understanding its properties is essential for analyzing transformations such as reflections.

Function Notation

Function notation, such as ƒ(x), is a way to denote a function and its output for a given input x. It allows for clear communication of mathematical ideas and operations. Understanding function notation is crucial for performing operations like finding reflections, as it helps in manipulating and interpreting the function correctly.