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Ch. 2 - Limits and Continuity
Hass - Thomas' Calculus 15th Edition
Hass15th EditionThomas' CalculusISBN: 9780137616077Not the one you use?Change textbook
All textbooksHass 15th EditionCh. 2 - Limits and ContinuityProblem 3i
Chapter 2, Problem 3i

Which of the following statements about the function y=f(x) graphed here are true, and which are false?


i. f(0)=1


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Verified step by step guidance
1
Examine the graph of the function y = f(x) at the point where x = 0. This involves identifying the y-coordinate of the point on the graph that corresponds to x = 0.
Determine the value of f(0) by observing the y-coordinate of the point on the graph where x = 0. This value is the output of the function when the input is 0.
Compare the observed value of f(0) with the given statement f(0) = 1. Check if the y-coordinate at x = 0 matches the value 1.
If the y-coordinate at x = 0 is equal to 1, then the statement f(0) = 1 is true. Otherwise, the statement is false.
Conclude whether the statement is true or false based on the comparison made in the previous step. This involves confirming the accuracy of the statement by referencing the graph.

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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 substituting a specific input value into a function to determine its output. For example, if f(x) is a function, then f(0) means we are looking for the value of the function when x equals 0. Understanding how to read and interpret function values from a graph is crucial for answering questions about specific points on the graph.
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Evaluating Composed Functions

Graph Interpretation

Graph interpretation is the ability to analyze and extract information from a visual representation of a function. This includes identifying key points, such as intercepts and local maxima or minima, as well as understanding the overall shape and behavior of the graph. In this context, it is essential to determine the value of f(0) by locating the point where the graph intersects the y-axis.
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Graphing The Derivative

True/False Statements

True/false statements require critical thinking to assess the validity of claims based on given information. In calculus, this often involves verifying whether a specific condition holds true for a function, such as checking if f(0) equals a certain value. This process typically involves both analytical skills and visual confirmation from the graph.
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Solving Exponential Equations Using Like Bases
Related Practice
Textbook Question

Which of the following statements about the function y=f(x) graphed here are true, and which are false?


c. limx→1 f(x) does not exist.


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Textbook Question

Limits and Continuity


Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.

f. | ƒ(t) |

Textbook Question

Which of the following statements about the function y=f(x) graphed here are true, and which are false?


a. limx→2 f(x) does not exist.


Textbook Question

Limits and Continuity


Suppose that ƒ(t) and ƒ(t) are defined for all t and that lim t → t₀ ƒ(t) = ―7 and lim (t → t₀) g (t) = 0 . Find the limit as t → t₀ of the following functions.

h. 1 / ƒ(t)

Textbook Question

Which of the following statements about the function y=f(x) graphed here are true, and which are false?


b. limx→2 f(x)=2


Textbook Question

Which of the following statements about the function y=f(x) graphed here are true, and which are false?


g. limx→1 f(x) does not exist.

1
views