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Questions and Answers
In the equation 3^(2x) - 2 = 3^(3x) + 4, how would you isolate x on one side?
In the equation 3^(2x) - 2 = 3^(3x) + 4, how would you isolate x on one side?
You would first rewrite the equation as 3^(2x) - 3^(3x) = 6 and then factor out the common term.
What does the character of the graph of f(x) = ax^n tell you about the degree n and the leading coefficient a if the graph has positive values for all x?
What does the character of the graph of f(x) = ax^n tell you about the degree n and the leading coefficient a if the graph has positive values for all x?
If f(x) is positive for all x, then n must be even and a must be positive.
Identify the type of symmetry exhibited by the graph of f(x) = ax^n when n is odd.
Identify the type of symmetry exhibited by the graph of f(x) = ax^n when n is odd.
The graph exhibits rotational symmetry about the origin.
How can you determine the intervals where f(x) is increasing for the graph of f(x) = ax^n?
How can you determine the intervals where f(x) is increasing for the graph of f(x) = ax^n?
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For the function f(x) = ax^n, what condition determines the presence of vertical asymptotes?
For the function f(x) = ax^n, what condition determines the presence of vertical asymptotes?
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Study Notes
Homework 8 Instructions
- Solutions to problems must be uploaded to Canvas before the deadline.
- Solutions must be organized, legible, and stapled.
- Points will be deducted for incomplete reasoning and disorganized work, even if answers are correct.
- Late submissions will not be accepted.
Problem 1: Symbolic Equations
- Solve the equations provided.
- These involve various algebraic manipulations to isolate the unknown variables.
Problem 2: Graph Analysis
- Use the graph of f(x) = axn to answer the following questions.
- (a) Determine if n is odd or even, and positive or negative. Justify.
- (b) Determine if the coefficient 'a' is positive or negative. Justify.
- (c) Identify the type of symmetry shown on the graph (e.g., even or odd). Explain your reasoning.
- (d) Find intervals where f(x) is positive. Explain.
- (e) Find intervals where f(x) is negative. Explain.
- (f) Determine if f(x) is increasing on any interval, and explain.
- (g) Determine if f(x) is decreasing on any interval, and explain.
- (h) Determine if there's a horizontal asymptote. If so, state the equation. Explain.
- (i) Determine if there's a vertical asymptote. If so, state the equation. Explain.
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