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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 3c
Chapter 2, Problem 3c

Use the graph of hh in the figure to find the following values or state that they do not exist. <IMAGE>
h(4)h\(\left\)(4\(\right\))

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Examine the graph of the function \( h(x) \) provided in the image to locate the point where \( x = 4 \).
Identify the corresponding \( y \)-value on the graph at \( x = 4 \). This \( y \)-value is \( h(4) \).
Check if the graph has a defined point at \( x = 4 \). If there is a point, note its \( y \)-coordinate.
If the graph has a hole or discontinuity at \( x = 4 \), then \( h(4) \) does not exist.
Conclude by stating the value of \( h(4) \) if it exists, or confirm that it does not exist based on the graph's behavior at \( x = 4 \).

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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 h(4) means finding the value of the function h when the input is 4. This process typically requires substituting the input into the function's formula or using a graph to identify the corresponding output.
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Evaluating Composed Functions

Graph Interpretation

Graph interpretation is the ability to read and analyze graphical representations of functions. It involves understanding the axes, identifying points on the graph, and determining the behavior of the function at specific values. For this question, one must look at the graph of h to find the value of h(4) visually.
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Graphing The Derivative

Existence of Function Values

The existence of function values refers to whether a function produces a valid output for a given input. In some cases, a function may not be defined at certain points, leading to the conclusion that a value does not exist. In this question, if the graph does not show a point at x=4, it indicates that h(4) does not exist.
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Average Value of a Function
Related Practice
Textbook Question

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

lim x→−1^− f(x)

Textbook Question

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

h(2)h\(\left\)(2\(\right\))

Textbook Question

What does it mean for a function to be continuous on an interval?

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Textbook Question

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

limx→4h(x){\(\displaystyle\]\lim\)_{x\(\to\)4}h\(\left\)(x\(\right\))}

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Textbook Question

21–30. Derivatives

a. Use limits to find the derivative function f' for the following functions f.

f(x) = 5x+2; a=1, 2

Textbook Question

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

f(−1)

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