Use the graph of in the figure to find the following values or state that they do not exist. <IMAGE>
Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
- 8. Definite Integrals4h 44m
- 9. Graphical Applications of Integrals2h 27m
- 10. Physics Applications of Integrals 3h 16m
- 11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
- 12. Techniques of Integration7h 39m
- 13. Intro to Differential Equations2h 55m
- 14. Sequences & Series5h 36m
- 15. Power Series2h 19m
- 16. Parametric Equations & Polar Coordinates7h 58m
1. Limits and Continuity
Introduction to Limits
Problem 5a
Textbook Question
Use the graph of f in the figure to find the following values or state that they do not exist. <IMAGE>
f(1)

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.

This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mPlay a video:
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:
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:
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:
Average Value of a Function
Watch next
Master Finding Limits Numerically and Graphically with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
Textbook Question