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Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 2 - Functions and GraphsProblem 33
Chapter 3, Problem 33

Use the graph of y = f(x) to graph each function g. g(x) = f(x)+2
Graph of y = f(x) showing two line segments with points at (-4,0), (0,0), (0,-2), and (4,-2) on a coordinate plane.

Verified step by step guidance
1
Understand that the function g(x) = f(x) + 2 represents a vertical shift of the original function f(x).
Recall that adding a constant to a function, like +2, shifts the entire graph of the function upward by that constant amount.
Take each point (x, y) on the graph of y = f(x) and transform it to a new point (x, y + 2) for the graph of g(x).
Plot these new points on the coordinate plane, maintaining the same x-values but increasing each y-value by 2.
Connect the new points smoothly, preserving the shape of the original graph, to complete the graph of g(x) = f(x) + 2.

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Key Concepts

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

Function Transformation

Function transformation involves changing the graph of a function in specific ways, such as shifting, stretching, or reflecting. In this case, adding a constant to the function, g(x) = f(x) + 2, shifts the graph vertically.
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Domain & Range of Transformed Functions

Vertical Shift

A vertical shift moves the entire graph of a function up or down without changing its shape. Adding 2 to f(x) raises every point on the graph by 2 units, so the graph of g(x) = f(x) + 2 is the graph of f(x) shifted up 2 units.
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Shifts of Functions

Graphing Functions

Graphing functions involves plotting points that satisfy the function's equation and connecting them smoothly. Understanding how transformations affect the graph helps in sketching the new function accurately based on the original graph.
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Graphs of Logarithmic Functions
Related Practice
Textbook Question

Find f−g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

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Textbook Question

Which graphs in Exercises 29–34 represent functions that have inverse functions?

Textbook Question

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3 b. f(10)

Textbook Question

Find ƒ+g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

Textbook Question

Evaluate each function at the given values of the independent variable and simplify. f(r)=r+6+3f(r)=\(\sqrt{r + 6}\)+3

a. f(−6)\(\text{a. }\)f(-6)

Textbook Question

Write the standard form of the equation of the circle with the given center and radius. Center (3, 2), r = 5

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