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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the degree of the function $$f(x) = 4x^3 + 2x$$?
💡 Hint: Look for the term with the biggest exponent.
Question 2
Easy
True or False: A cubic function can have four real roots.
💡 Hint: Think about the maximum number of times a cubic function can cross the x-axis.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the maximum number of real roots a cubic function can have?
- 1
- 2
- 3
- 4
💡 Hint: Remember the highest degree defines the maximum number of x-intercepts.
Question 2
True or False: A cubic function always has at least one real root.
- True
- False
💡 Hint: Think about the nature of continuous functions.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function $$f(x) = 3x^3 - 12x + 9$$, find its real roots and describe the graph.
💡 Hint: Use x-value substitution to determine roots and sketch based on end behavior.
Question 2
Analyze the end behavior for the cubic function $$f(x) = -2x^3 + 5x^2 + 4$$. Explain what happens as x approaches infinity and negative infinity.
💡 Hint: Look at the leading coefficient's sign to predict the graph's direction.
Challenge and get performance evaluation