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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 55
Chapter 3, Problem 55

In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. (go f) (-1)


Two tables showing values of functions f and g with inputs x and corresponding outputs f(x) and g(x) for specific x values.

Verified step by step guidance
1
Identify the composite function to evaluate: (g \(\circ\) f)(-1), which means g(f(-1)).
Find the value of f(-1) from the first table. Look for the row where x = -1 and note the corresponding f(x) value.
Using the value found for f(-1), substitute it into the function g. This means you will look for g(f(-1)) in the second table by finding the row where x equals the value of f(-1).
Find the corresponding g(x) value from the second table for the x value found in the previous step.
The value you find for g(x) in the last step is the value of the composite function (g \(\circ\) f)(-1).

Key Concepts

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

Function Notation and Evaluation

Function notation, such as f(x), represents the output of a function f for an input x. Evaluating a function means finding the output value corresponding to a specific input by using the given function rule or table. For example, from the table, f(-1) = 1 means when x = -1, the output of f is 1.
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Evaluating Composed Functions

Composite Functions

A composite function (g o f)(x) means applying function f first to x, then applying function g to the result of f(x). It is written as g(f(x)). To evaluate (g o f)(-1), first find f(-1), then use that output as the input for g.
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Function Composition

Using Tables to Evaluate Functions

When functions are defined by tables, you find the output by locating the input value in the table and reading the corresponding output. For composite functions, use the output from the first function's table as the input for the second function's table.
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Evaluating Composed Functions
Related Practice
Textbook Question

Use the vertical line test to identify graphs in which y is a function of x.

Textbook Question

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² – 10x – 6y – 30 = 0

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Textbook Question

Graph each equation in a rectangular coordinate system. f(x) = 1

Textbook Question

In Exercises 55–59, use the graph of to graph each function g.

g(x) = f(x + 2) + 3

Textbook Question

In Exercises 51–54, graph the given square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of x that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = √x (x = 0, 1, 4, 9) and g (x) = √(x + 2) (x = = −2, −1, 2, 7)

Textbook Question

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. g(x) = (x − 2)²