Sketching One Period of a Sine Function
Sketching one period of a transformed sine graph
Properties of a Sine Function
Author: Doan Nguyen
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Reveal Answer" to reveal the answer to the problem.
Problem: Find the amplitude, period, phase shift, and vertical shift of:\[
y=2\sin(3x-\frac{9\pi}{4})-5
\]
Amplitude: \(2\)
Period: \(\dfrac{2\pi}{3}\)
Phase Shift: \(\dfrac{3\pi}{4}\)
Vertical Shift: \(-5\)
Period: \(\dfrac{2\pi}{3}\)
Phase Shift: \(\dfrac{3\pi}{4}\)
Vertical Shift: \(-5\)
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Adding Rational Expressions
Adding two rational expressions and then simplifying the answer
Holes and Asymptotes of Rational Functions
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Holes and Asymptotes of Rational Functions (2)
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Matching a Rational Function with its Graph
Matching a rational function with its graph
Roots of a Quadratic
Using the quadratic formula to find the roots of a function
Roots of a Polynomial
Finding the roots of a cubic polynomial
Roots of a Square Root Function
Finding the roots of a square root function
Roots of a Function with an Absolute Value
Finding the roots of a function with an absolute value
Domain of a Rational Function
Finding the domain of a rational function
Domain of a Rational Function (2)
Finding the domain of a rational function
Domain of Function with Roots
Finding the domain of a function with a fraction and radicals
Domain of a Square Root Function
Finding the domain of a function with a quadratic inside a square root
Composition of Polynomial Functions
Finding the composition of two functions
Function Composition with a Rational Function
Finding the composition of a rational function and a quadratic
Composition of Logarithmic and Exponential Functions
Finding the composition of two functions with exponentials and logarithms
Composition of Square Root and Power Functions
Finding the composition of two functions with a square root and a fractional exponent
Composition of Cube Root and Power Functions
Finding the composition of two functions with a cube root and a fractional exponent
Inverse of a Linear Function
Finding the inverse of a linear function and its domain
Inverse of a Square Root Function
Finding the inverse of a square root function and its domain
Inverse of a Rational Function
Finding the inverse of a rational function and its domain
Inverse of a Rational Function (2)
Finding the inverse of a rational function and its domain
Difference Quotient of a Quadratic
Finding and simplifying the difference quotient for a quadratic function
Difference Quotient of a Rational Function
Finding and simplifying the difference quotient for a rational function
Difference Quotient of a Square Root Function
Finding and simplifying the difference quotient for a square root function
Solving an Inequality with a Polynomial
Solving an inequality with a polynomial by factoring and using a sign diagram
Solving an Inequality with a Rational Function
Solving an inequality with a rational expression by factoring and using a sign diagram
Solving an Inequality with a Sum of Rational Functions
Solving an inequality with two rational expressions using a sign diagram
Solving an Inequality with by Finding a Least Common Denominator
Solving an inequality with a rational expression using a sign diagram
Solving an Inequality with a Quadratic Function
Solving an inequality with a quadratic by factoring and using a sign diagram
Absolute Maximum or Minimum of a Quadratic
Finding the absolute maximum or absolute minimum of a quadratic
Standard Form of a Quadratic
Writing the standard form of quadratic function given its vertex and one other point
Component Form and Magnitude of a Vector
Finding the component form and magnitude for a vector between two points
Vector Addition and Subtraction and Scalar Multiplication
Performing calculations with vectors including addition, subtraction, and scalar multiplication
Dot Product
Calculating the dot product for three pairs of vectors
Finding a Unit Vector
Finding a unit vector in the direction of a given vector
Solving a System of Equations
Solving a system of two linear equations using the method of substitution
Solving a System of Equations (2)
Solving a system of two linear equations using the method of substitution
Solving a System of Equations (3)
Solving a system of two linear equations
Solving a System of Nonlinear Equations
Solving a system on two equations where one is linear and one is quadratic
An Equation with an Exponential Function
Solving a equation with an exponential function
An Equation with Exponential Functions of Different Bases
Solving an equation with two exponential functions with different bases
Factoring a Quadratic-Like Equation with Exponentials
Solving an equation with exponential functions by factoring
Factoring an Equation with Exponentials
Solving a equation with exponential functions by factoring
Population Model with Exponential Growth
Finding the size of a population of rabbits with exponential growth
Population Model with Exponential Decay
Finding the size of a population of rabbits with exponential decay
Horizontal Asymptote of an Exponential Function
Finding the horizontal asymptote of an exponential function
Horizontal Asymptote of an Exponential Function (2)
Finding the horizontal asymptote of an exponential function
Horizontal Asymptote of an Exponential Function (3)
Finding the horizontal asymptote of an exponential function
Expanding a Logarithmic Expression
Expanding a logarithmic expression using logarithm properties
Condensing a Logarithmic Expression
Condensing logarithmic expressions into a single logarithm
Evaluating Logarithmic Expressions
Finding the exact value of logarithms using logarithmic properties
Vertical Asymptote of a Logarithmic Function
Finding the vertical asymptote of a logarithmic function
Vertical Asymptote of a Logarithmic Function (2)
Finding the vertical asymptote of a logarithmic function
Domain and x-intercepts of a Logarithmic Function
Finding the domain and x-intercepts of a logarithmic function
Domain and x-intercepts of a Logarithmic Function (2)
Finding the domain and x-intercepts of a logarithmic function
Solving an Equation with Logarithms
Solving a logarithmic equation using properties of logarithms
Solving an Equation with a Logarithmic Function
Solving a logarithmic equation using properties of logarithms
A Composition of Tangent and Arccosine
Evaluating a composition of tangent and arccosine
WIR 20B M152 V51
Determining if a series converges or diverges
WIR 20B M152 V59
Using the limit comparison test to determine if a series converges or diverges
WIR 20B M152 V62
Using the Alternating Series Test to determine if a series converges or diverges
WIR 20B M152 V63
Using the Alternating Series Test to determine if a series converges or diverges
Generating and Plotting Sequences in Python
Using Python to numerically, graphically, and analytically find the limit of a sequence
Review for the Common Exam: MATH 151 Exam 1 Review Problems 10-13
Review of vector functions and parametric equations