# Precalculus

### Featured Answers

### Algebraic Modeling

- Graphing Data
- Analyzing Data
- Solving Problems Algebraically and Graphically
- Domain
- Range
- Boundedness
- Local and Absolute Extrema
- Symmetry
- Asymptotes
- End Behavior
- Introduction to Twelve Basic Functions
- Function Composition
- Modeling with Functions
- Linear Functions and Graphs
- Average Rate of Change
- Linear Correlation and Modeling
- Graphing Quadratic Functions
- Applications of Quadratic Functions
- Linear and Quadratic Functions on a Graphing Calculator
- Completing the Square
- The Quadratic Formula
- Graphing Power Functions
- Modeling with Power Functions
- Power Functions and Variation on a Graphing Calculator
- Graphing Polynomial Functions
- End Behavior
- Zeros
- Intermediate Value Theorem
- Polynomial Functions of Higher Degree on a Graphing Calculator
- Zero Factor Property
- Long Division of Polynomials
- Remainder and Factor Theorems
- Synthetic Division
- Rational Zeros
- Upper and Lower Bounds
- Real Zeros of Polynomials on a Graphing Calculator
- Fundamental Theorem of Algebra
- Complex Conjugate Zeros
- Factoring Real Number Coefficients
- Complex Zeros on a Graphing Calculator
- Transformations of the Reciprocal Function
- Limits - End Behavior and Asymptotes
- Graphing Rational Functions on a Graphing Calculator
- Extraneous Solutions
- Solving Rational Equations on a Graphing Calculator
- Sign Charts
- Polynomial Inequalities
- Solving Rational Inequalities on a Graphing Calculator
- Exponential and Logistic Graphs
- The Natural Base e
- Population Models
- Exponential and Logistic Functions on a Graphing Calculator
- Scientific Notation
- Constant Percentage and Exponentials
- Exponential Growth and Decay
- Modeling Population with Regression on a Graphing Calculator
- Other Logistic Models
- Exponential and Logistic Modeling on a Graphing Calculator
- Logarithm-- Inverse of an Exponential Function
- Common Logs
- Functions with Base b
- Natural Logs
- Orders of Magnitude
- Logarithmic Models
- Newton's Law of Cooling
- 2-D Vectors
- Vector Operations
- Unit Vectors
- Direction Angles
- The Dot Product
- Angle between Vectors
- Vector Projection
- Work
- The Polar Coordinate System
- Converting Coordinates from Rectangular to Polar
- Converting Coordinates from Polar to Rectangular
- Converting Equations from Polar to Rectangular
- Finding Distance Between Polar Coordinates
- Rose Curves
- Cardioid Curves
- Limacon Curves
- Complex Number Plane
- Trigonometric Form of Complex Numbers
- Multiplication of Complex Numbers
- Division of Complex Numbers
- Powers of Complex Numbers
- Roots of Complex Numbers
- Solving by Substitution
- Solving by Elimination
- Solving Graphically
- Addition of Matrices
- Subtraction of Matrices
- Multiplication of Matrices
- Identity Matrix
- Inverse Matrix
- Determinant of a Square Matrix
- Cramer's Rule
- Gaussian Elimination
- Elementary Row Operations
- Reduced Row Echelon Form
- Solving a System of Equations Using a Matrix
- Partial Fraction Decomposition (Linear Denominators)
- Partial Fraction Decomposition (Irreducible Quadratic Denominators)
- Graphing Systems of Inequalities
- Linear Programming
- Standard Form of the Equation
- Vertex Form of the Equation
- Identify Critical Points
- Graphing Parabolas
- Standard Form of the Equation
- General Form of the Equation
- Identify Critical Points
- Graphing Ellipses
- Standard Form of the Equation
- General Form of the Equation
- Identify Critical Points
- Graphing Hyperbolas
- Graphing Conic Sections Algebraically
- Graphing Conic Sections on a Graphing Calculator
- Translation of a Conic Section
- Rotation of a Conic Section
- Finding the Angle of Rotation
- Finding the Coefficients for a Conic in a Rotated System
- Writing Polar Equations for Conic Sections
- Analyzing Polar Equations for Conic Sections
- 3-D Coordinates
- Finding Distance and Midpoint
- Equation of a Sphere
- Planes
- Vectors in Space
- Lines in Space
- Powers of the Binomial
- Pascal's Triangle and Binomial Expansion
- The Binomial Theorem
- Factorial Identities
- Infinite Sequences
- Limits of Infinite Sequences
- Arithmetic Sequences
- Geometric Sequences
- Working with Sequences on a Graphing Calculator
- Summation Notation
- Sums of Arithmetic Sequences
- Sums of Geometric Sequences
- Infinite Series
- Convergence of Geometric Series
- Average Velocity
- Instantaneous Velocity
- The Derivative by Definition
- Definition of the Tangent Line
- Distance from a Constant Velocity
- Distance from a Changing Velocity
- Connection to Areas
- The Definite Integral
- Concepts and Informal Definition of a Limit
- Properties of Limits
- Limits of Continuous Functions
- One-Sided Limits
- Two-Sided Limits
- Limits Involving Infinity
- Graphing Trigonometric Functions with Domain and Range
- Graphing Trigonometric Functions with Critical Points
- Graphing Trigonometric Functions with Translations and Asymptotes
- Graphing Sine and Cosine
- Translations of Sinusodial Graphs
- What it mean to say an infinite series converges?
- What is the graph of the polynomial function #x^4 + 1/3x^3 + 1/2x^2 - 10#?
- How do I find the limit of a rational function?
- How to find the scientific notation for a negative number?
- How do I work with natural logarithms in Excel?
- How do I find the three cube roots of unity?
- How do I rotate a hyperbola from opening vertically to opening horizontally?
- Is matrix multiplication commutative?
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- How can you simplify #1/(3sqrt(1-x^2/9))#?
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- What is the difference between Precalculus and Calculus ?
- What is meant by the "base" and "exponent" of a number and how do these relate to logarithms?
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- Why does a line have infinitely many sets of direction ratios?
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- Given that #z# is a complex number and that #t# is real, and that #z = 2 + 3t + i(4 - t)#. Show that the minimum value of #|z|# is #(7sqrt(10))/5#?
- #z # is a complex number. Show that the equation #z^4 + z + 2= 0# cannot have a root #z# such that #|z|<1#?
- #itheta = 7 - 4i# Find #theta# ?
- Show that the roots of the equation #16x^4 - 20x^2 + 5= 0# are #cos((kx)/10) #for #k = 1,3,7 # and # 9# And Deduce that #cos^2(pi/10)cos^2((3pi)/10) = 5/16#?
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- How do you solve for x in #2^x = 5^(x - 2)#?
- How do you solve #(1/7)^x-3=343#?
- How do you solve #y = log^3(78.5)#?
- Let # f(x)= (x+3)/(x^2 -4x-12)# and #g(x)=sqrt(3-x)#, how do you find each of the compositions and domain and range?
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- How do you write the equation of a transformed graph?
- How can I simplify sin2xcosx+cos2xsinx?
- How can I determine the exact values for tan75?
- How can I find c and d if #8 cos (theta - pi / 3)=c sin theta + d cos theta#?
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- How do you solve #e^(2x)+8e^x+12 = 0# ?
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- A polynomial function #f(x) = ax^3+bx^2-28x+15# is divisible by #(x+3)# and #f(x)+60# is divisible by #(x-3)#. How do you find #a, b# and solve #f(x) = 0# ?
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- How do you sum the series #1+a+a^2+a^3+...+a^n#?
- (f○g)(x)=√(1-3x²)/(2x-8) and (g○f)(x)=(1-3x²)/(3-2x²) . How to find f(g(4))?
- How to determine whether f(x)3sin2x +5 is one-to-one function. How to find the inverse of the function?
- How to determine whether f(x)= 2x²-4x -1 is one to one function given that x is more than or equal to 1?
- For what values of #x# is #sin x = cos x# ?
- How do you use synthetic division to find all roots of #x^3 + 5x^2 + 3x -9 = 0#?
- Let #s(x) = x^2 + 2x + 3x# and #t(x) =sqrt( x+4)# how do you find #(s( t)) (6)#?
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- How do you factor #2x^3+162# ?
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