Textbook Question
Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (4, 7) and (8, 10)
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 3, Problem 1
Use the graph of y = f(x) to graph each function g.
g(x) = f(x)+1
Verified step by step guidance1
Identify the original function f(x) from the graph. Here, f(x) is a horizontal line segment from (1, -3) to (4, -3).
Understand the transformation for g(x) = f(x) + 1. This means you add 1 to every y-value of f(x).
Apply the transformation to the endpoints of the line segment: For (1, -3), calculate the new y-value as -3 + 1.
Similarly, for (4, -3), calculate the new y-value as -3 + 1.
Plot the new points with the updated y-values and draw a horizontal line segment connecting them to graph g(x).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Transformation - Vertical Shift
A vertical shift moves the graph of a function up or down without changing its shape. Adding a constant to the function, as in g(x) = f(x) + 1, shifts the entire graph of f(x) upward by that constant value. For example, if f(x) = -3, then g(x) = -3 + 1 = -2.
Recommended video:
5:34
Shifts of Functions
Graphing Piecewise or Segment Functions
When graphing functions defined on specific intervals, such as a line segment from (1, -3) to (4, -3), it is important to only plot points within the given domain. The graph of g(x) = f(x) + 1 will maintain the same domain but shift the y-values accordingly.
Recommended video:
5:26Graphs of Logarithmic Functions
Coordinate Points and Plotting
Understanding how to plot points on the coordinate plane is essential. Each point (x, y) represents a location where x is the horizontal position and y is the vertical position. For g(x) = f(x) + 1, each y-coordinate of f(x) is increased by 1, so points like (1, -3) become (1, -2).
Recommended video:
Guided course
05:10Graphs & the Rectangular Coordinate System
Related Practice
Textbook Question
Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (2, 3) and (14, 8)
2
views
Textbook Question
Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 4x and g(x) = x/4
5
views