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Precalculus - Concept Videos
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All Topics
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Graphing parametric functions in x-y planes
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Comparing parametric and Cartesian forms
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Identifying parametric equations for simple curves
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Calculating derivatives of parametric equations
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Understanding tangent lines in parametric graphs
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Exploring relationships between x and y changes
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Adding and subtracting vectors
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Computing magnitudes and directions
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Representing motion using vector components
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Graphing 2D vector fields
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Understanding velocity and acceleration in vector form
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Combining vectors with scalar functions
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Basics of matrix addition and multiplication
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Representing linear equations with matrices
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Analyzing matrix properties algebraically
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Understanding matrix-based transformations
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Verifying transformations using input-output pairs
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Connecting linear transformations to geometry
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Solving systems of equations with inverse matrices
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Verifying solutions using determinants
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Simplifying complex systems algebraically
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Identifying transformations of logarithmic functions
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Solving logarithmic equations symbolically
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Defining logarithmic bases and their properties
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Expanding and simplifying logarithmic terms
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Combining terms with the same base
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Factoring logarithms for solving equations
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Solving inequalities involving logarithms
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Validating solutions using substitution
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Using exponentiation to verify logarithmic solutions
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Representing exponential data with semi-log scales
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Identifying linear trends in transformed data
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Comparing semi-log plots to regular plots
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Recognizing differences in arithmetic sequences
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Identifying ratios in geometric sequences
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Connecting sequences to linear and exponential functions
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Identifying linear growth or decay rates
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Comparing linear vs. exponential rates of increase
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Understanding when exponential models are appropriate
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Understanding domain and range of exponential functions
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Analyzing transformations: vertical and horizontal shifts
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Exploring asymptotic behavior in exponential graphs
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Simplifying exponential expressions using rules of exponents
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Factoring exponential terms in equations
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Expanding powers for simplification
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Representing patterns algebraically
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Validating assumptions in exponential equations
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Generalizing growth models without specific real-world scenarios
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Testing linear vs. exponential models for fit
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Comparing residuals to determine accuracy
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Analyzing errors in model assumptions
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Combining two exponential functions
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Using compositions for recursive sequences
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Exploring commutativity in function compositions
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Identifying conditions for inverses
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Verifying inverse relationships algebraically
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Sketching inverse functions on a graph
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Expanding logarithmic terms using rules of logs
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Simplifying nested logarithms
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Converting between logarithmic and exponential forms
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Analyzing inverse symmetry in graphs
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Understanding logarithms as inverses of exponents
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Exploring how inverse transformations affect function shapes
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Simplifying rational functions to reveal holes
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Testing function continuity at holes
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Identifying removable discontinuities
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Factoring and simplifying expressions
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Expanding rational expressions
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Verifying equivalency through algebraic manipulation
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Horizontal and vertical shifts
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Stretching and compressing functions
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Reflecting across axes
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Choosing appropriate polynomial or rational models
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Testing assumptions through equation constraints
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Analyzing limitations of chosen models
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Writing polynomial and rational models
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Simplifying derived models for analysis
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Interpreting model parameters algebraically
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Identifying relationships between variables
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Representing co-variation with graphs and tables
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Recognizing proportional relationships
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Definition and calculation of average rate of change
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Interpreting instantaneous rate of change
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Slope as a measure of rate in linear functions
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Identifying constant rates in linear models
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Analyzing variable rates in quadratic functions
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Determining intervals of increase and decrease
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Graphical representation of polynomial behaviors
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Understanding the degree's role in rate analysis
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Identifying turning points and critical points
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Finding complex zeros using the quadratic formula
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Factoring polynomials with real and complex roots
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Verifying solutions with synthetic division
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Predicting end behavior using leading coefficients
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Determining symmetry in polynomial graphs
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Understanding multiplicities of roots
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Determining horizontal asymptotes
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Analyzing degrees of numerator and denominator
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Identifying oblique asymptotes
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Finding zeros in rational functions
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Multiplicity and their impact on graph shape
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Using synthetic and long division
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Defining vertical asymptotes algebraically
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Testing continuity near asymptotes
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Identifying behaviors approaching vertical asymptotes
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Understanding cycles in functions
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Representing periodic intervals
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Exploring periodicity in graphs
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Computing trigonometric ratios using the unit circle
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Verifying identities involving sine, cosine and tangent
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Exploring co-functions and their relationships
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Computing exact values for common angles
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Understanding reflection and symmetry properties
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Analyzing periodic properties of sine and cosine
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Graphing sine and cosine with amplitude and period
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Identifying shifts in sine and cosine graphs
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Exploring relationships between graphs of sine and cosine
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Graphing tangent over its domain
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Identifying vertical asymptotes in tangent graphs
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Analyzing tangent transformations
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Determining restricted domains of inverses
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Using inverse functions to solve equations
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Verifying identities with inverses
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Solving multi-angle equations
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Exploring periodic solutions in equations
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Analyzing domain-specific inequalities
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Graphing reciprocal functions of sine, cosine and tangent
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Identifying domains and asymptotes
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Verifying reciprocal relationships in identities
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Using Pythagorean identities to simplify
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Verifying equivalences through substitution
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Rewriting expressions for computational ease
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Converting Cartesian equations to polar form
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Graphing polar coordinates
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Analyzing polar symmetry and rotations
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Graphing cardioids, roses and spirals
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Analyzing periodicity and intersections in polar graphs
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