Podcast
Questions and Answers
A cubic polynomial has roots at $x = -2$, $x = 1$, and $x = 3$. Which of the following could be the polynomial?
A cubic polynomial has roots at $x = -2$, $x = 1$, and $x = 3$. Which of the following could be the polynomial?
- $x^3 - 2x^2 - 5x + 6$
- $x^3 - 6x^2 + 11x - 6$
- $x^3 - 2x^2 - x + 6$ (correct)
- $x^3 + 4x^2 + x - 6$
Which of the following statements is true regarding the graph of the rational function $f(x) = \frac{x+1}{(x-2)(x+3)}$?
Which of the following statements is true regarding the graph of the rational function $f(x) = \frac{x+1}{(x-2)(x+3)}$?
- The graph has a vertical asymptote at $x = -1$ and intercepts at $x=2$ and $x=-3$.
- The graph has vertical asymptotes at $x = -2$ and $x = 3$, and an x-intercept at $x = 1$.
- The graph has a vertical asymptote at $x = 2$ and $x = -3$, and no x-intercepts.
- The graph has vertical asymptotes at $x = 2$ and $x = -3$, and an x-intercept at $x = -1$. (correct)
How does the graph of $y = 2^{x+1} - 3$ compare to the graph of $y = 2^x$?
How does the graph of $y = 2^{x+1} - 3$ compare to the graph of $y = 2^x$?
- Shifted right 1 unit and down 3 units.
- Shifted left 1 unit and down 3 units. (correct)
- Shifted right 1 unit and up 3 units.
- Shifted left 1 unit and up 3 units.
Solve for $x$: $3^{2x+1} = 81$
Solve for $x$: $3^{2x+1} = 81$
Given the equation $\log_2(x) + \log_2(x-2) = 3$, find the value of $x$.
Given the equation $\log_2(x) + \log_2(x-2) = 3$, find the value of $x$.
Suppose $5,000 is invested in an account that pays 6% annual interest compounded quarterly. What will be the balance after 3 years?
Suppose $5,000 is invested in an account that pays 6% annual interest compounded quarterly. What will be the balance after 3 years?
A store sells apples and bananas. On Monday, they sold 30 apples and 12 bananas for a total of $18. On Tuesday, they sold 20 apples and 8 bananas for a total of $12. What is the price of one apple?
A store sells apples and bananas. On Monday, they sold 30 apples and 12 bananas for a total of $18. On Tuesday, they sold 20 apples and 8 bananas for a total of $12. What is the price of one apple?
What is the partial fraction decomposition of $\frac{5x - 1}{(x-1)(x+2)}$?
What is the partial fraction decomposition of $\frac{5x - 1}{(x-1)(x+2)}$?
Which point satisfies the following system of inequalities: $y > x^2$ and $y < -x + 6$?
Which point satisfies the following system of inequalities: $y > x^2$ and $y < -x + 6$?
The population of a town is modeled by the equation $P(t) = 1000e^{0.05t}$, where $t$ is the number of years since 2020. In what year will the population reach 2000?
The population of a town is modeled by the equation $P(t) = 1000e^{0.05t}$, where $t$ is the number of years since 2020. In what year will the population reach 2000?
Flashcards
Factoring Cubic Polynomials
Factoring Cubic Polynomials
A method to factor cubic polynomials or construct a polynomial from its roots.
Graphing Rational Functions
Graphing Rational Functions
Graphing rational functions including identifying vertical asymptotes and intercepts.
Graphing Exponential/Log Functions
Graphing Exponential/Log Functions
Graphing exponential or logarithmic functions including shifts, reflections, and transformations.
Solving Exponential/Log Equations
Solving Exponential/Log Equations
Signup and view all the flashcards
Laws of Logs for Solving Equations
Laws of Logs for Solving Equations
Signup and view all the flashcards
Compound Interest
Compound Interest
Signup and view all the flashcards
System of Two Equations
System of Two Equations
Signup and view all the flashcards
Partial Fractions Decomposition
Partial Fractions Decomposition
Signup and view all the flashcards
Graphing System of Inequalities
Graphing System of Inequalities
Signup and view all the flashcards
Study Notes
- Exam 3 is on Wednesday and covers sections 3.4 up to 6.5.
Factoring Cubic Polynomials
- Utilize synthetic division to factor cubic polynomials.
- Alternatively, construct a polynomial if given its roots.
Graphing Rational Functions
- Graph rational functions, with an emphasis on those having two vertical asymptotes.
- Identify and provide asymptotes and intercepts accurately.
Graphing Exponential and Logarithmic Functions
- Graph exponential or logarithmic functions incorporating shifts.
- Be prepared for exponential functions reflected upside down.
Solving Exponential and Log Equations
- Solve standard exponential or logarithmic equations.
- Employ the one-to-one property.
Solving Equations with Laws of Logs
- Use the laws of logarithms to solve various equations.
Compound Interest
- Problems involving compound interest calculations.
Systems of Two Equations
- Solve systems of two equations, with a focus on word problems.
Partial Fractions Decomposition
- Perform partial fractions decomposition.
Graphing Systems of Inequalities
- Graph systems of inequalities.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
