Math Problem Statement
graph 1/x-3
Solution
To graph the function , we will follow these steps:
-
Identify the basic graph: The basic graph of is a hyperbola with two asymptotes:
- The vertical asymptote is at , since division by zero is undefined.
- The horizontal asymptote is at , because as becomes large (either positive or negative), approaches zero.
-
Shift the graph: The given function shifts the basic graph of vertically by 3 units downward. This means that the horizontal asymptote will shift from to .
-
Plot key points:
- As , , and as , (the graph approaches the vertical asymptote at from either side).
- As , , and similarly, as , .
-
Plot a few specific points: Choose values of and calculate . For example:
-
Sketch the graph: Now, plot these points and sketch the asymptotes. The graph will approach the asymptotes as moves away from zero, curving downward toward .
Would you like me to create the graph visually for you? Let me know if you want more details or further explanations.
Here are 5 related questions you might find interesting:
- How do vertical and horizontal asymptotes impact the graph of rational functions?
- What happens if we change the constant term in ?
- How would the graph of differ from the one we graphed?
- What are the domain and range of ?
- How do transformations affect the parent function ?
Tip: When graphing rational functions, always start by identifying asymptotes and a few key points to guide the shape of the graph!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Rational Functions
Graphing Functions
Asymptotes
Transformations
Formulas
f(x) = 1/x - 3
Theorems
Asymptote Theorem
Transformation of Functions
Suitable Grade Level
Grades 9-12
Related Recommendation
Understanding Rational Functions: f(x) = 1/x - 3 with Asymptotes and Intercepts
Graphing Rational Functions with Asymptotes and Key Properties
Graphing and Analyzing the Rational Function f(x) = 1/x^2
Graph of Rational Function y = (6x - 1) / 3x with Asymptotes
Graphing Rational Function f(x) = 3 / (2x + 1)