Skip to main content
Ch. 2 - Limits
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Not the one you use?Change textbook
All textbooksBriggs 3rd EditionCh. 2 - LimitsProblem 5a
Chapter 2, Problem 5a

Use the graph of ff in the figure to find the following values or state that they do not exist. <IMAGE>
f(1)f\(\left\)(1\(\right\))

Verified step by step guidance
1
Identify the point on the graph where the x-coordinate is 1. This is the point where you will evaluate the function f(x).
Observe the y-coordinate of the point on the graph corresponding to x = 1. This y-coordinate is the value of f(1).
Check if the graph has a defined point at x = 1. If there is a hole or discontinuity at this point, then f(1) does not exist.
If the point is defined and there is no discontinuity, then the y-coordinate at x = 1 is the value of f(1).
Conclude by stating the value of f(1) if it exists, or state that it does not exist if the graph is undefined at x = 1.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

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

Function Evaluation

Function evaluation involves determining the output of a function for a specific input value. In this case, evaluating f(1) means finding the value of the function f at x = 1. This process requires understanding how to read the graph of the function to identify the corresponding y-value when x is 1.
Recommended video:
4:26
Evaluating Composed Functions

Graph Interpretation

Graph interpretation is the ability to analyze and extract information from a visual representation of a function. This includes recognizing key features such as intercepts, peaks, and troughs, as well as understanding the behavior of the function at specific points, which is crucial for answering questions about function values.
Recommended video:
06:15
Graphing The Derivative

Existence of Function Values

The existence of function values refers to whether a function is defined at a particular input. For instance, if the graph does not have a point at x = 1, then f(1) does not exist. Understanding this concept is essential for determining if the requested values can be found or if they are undefined.
Recommended video:
06:37
Average Value of a Function
Related Practice
Textbook Question

Use the graph of ff in the figure to find the following values or state that they do not exist. <IMAGE>

f(0)f\(\left\)(0\(\right\))

Textbook Question

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→3 f(x)

2
views
Textbook Question

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>

lim x→3^+ f(x)

5
views
Textbook Question

Determine the following limits at infinity.


lim x→ ∞ x^−6

1
views
Textbook Question

Estimate lim θ→0 sin 2θ / sin θ using the graph in part (a).

Textbook Question

Determine the following limits at infinity.


lim x→−∞ x^−11

8
views