Podcast
Questions and Answers
What is a key characteristic of all the polynomial functions listed when graphed?
What is a key characteristic of all the polynomial functions listed when graphed?
- They all have horizontal asymptotes.
- They all have the same y-intercept.
- They all pass through the origin. (correct)
- They all exhibit oscillating behavior.
How does the end behavior of even-degree polynomials differ from that of odd-degree polynomials?
How does the end behavior of even-degree polynomials differ from that of odd-degree polynomials?
- Even-degree polynomials rise on both ends while odd-degree polynomials have opposite behavior. (correct)
- Even-degree polynomials lead towards infinity in opposite directions.
- Odd-degree polynomials exhibit linear growth as they approach the ends.
- Odd-degree polynomials can only approach zero at both ends.
What effect does adding +1 to the function f(x) = x³ have on the graph?
What effect does adding +1 to the function f(x) = x³ have on the graph?
- It causes a horizontal shift to the left.
- It results in a vertical shift upwards. (correct)
- It reflects the graph across the x-axis.
- It alters the degree of the polynomial.
What transformation does the equation g(x) = (x - 2)⁴ represent compared to g(x) = x⁴?
What transformation does the equation g(x) = (x - 2)⁴ represent compared to g(x) = x⁴?
What effect does the transformation in h(x) = -(x + 5)⁵ - 2 have on the original function p(x) = x⁵?
What effect does the transformation in h(x) = -(x + 5)⁵ - 2 have on the original function p(x) = x⁵?
Which polynomial function has the steepest increase near the origin based on its degree?
Which polynomial function has the steepest increase near the origin based on its degree?
How do the graphs of the even-degree and odd-degree polynomials differ in terms of symmetry?
How do the graphs of the even-degree and odd-degree polynomials differ in terms of symmetry?
What is the maximum number of x-intercepts that the function g(x) = (x - 2)⁴ can have?
What is the maximum number of x-intercepts that the function g(x) = (x - 2)⁴ can have?
When observing the end behavior of l(x) = x⁶, what can be concluded about its behavior as x approaches negative infinity?
When observing the end behavior of l(x) = x⁶, what can be concluded about its behavior as x approaches negative infinity?
What effect does the graph of h(x) = -(x + 5)⁵ - 2 have compared to the base function p(x) = x⁵?
What effect does the graph of h(x) = -(x + 5)⁵ - 2 have compared to the base function p(x) = x⁵?
Flashcards
End Behavior of Polynomials
End Behavior of Polynomials
For odd degree polynomials, the graph falls to the left and rises to the right, or vice versa. For even degree polynomials, the graph rises to the left and rises to the right, or it falls to the left and falls to the right.
X-Intercepts of Polynomials
X-Intercepts of Polynomials
The maximum number of times the graph of a polynomial function can cross the x-axis is equal to the degree of the polynomial. This is because the degree of a polynomial represents the maximum number of roots or x-intercepts it can have.
Odd vs Even Degree Polynomial X-Intercepts
Odd vs Even Degree Polynomial X-Intercepts
A polynomial function of odd degree always crosses the x-axis at least once, while a polynomial function of even degree may or may not cross the x-axis.
Turning Points of Polynomial Functions
Turning Points of Polynomial Functions
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Transformations of Polynomial Graphs
Transformations of Polynomial Graphs
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X-intercept of a Polynomial
X-intercept of a Polynomial
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Odd vs Even Degree Polynomials and X-Intercepts
Odd vs Even Degree Polynomials and X-Intercepts
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