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Subtracting Functions - Formula, Rules & Examples

Derive proofs involving properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems involving properties of angles and triangles

Unit circle

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Angles in a circle

Determining non-permissible values for trig expressions

Triangles

Solve problems involving cosine law and sine law, including ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Analyze and prove conjectures using inductive and deductive reasoning to solve problems

Null hypothesis and alternative hypothesis

Proving claims

Confidence levels, significance levels and critical values

Test statistics

Analyze puzzles and games involving spatial reasoning using problem-solving strategies

Line symmetry

Rotational symmetry and transformations

Solve problems involving application of rates

Direct variation

Identifying direct variations

Rate of change

Applications of linear relations

Solve problems involving scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Understand relationships among scale factors, areas, surface areas, and volumes of similar 2-D shapes and 3-D objects

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Model and solve problems involving systems of linear inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Inequalities of combined functions

Inequalities of Combined Functions

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of quadratic functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Inverse functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Demonstrate understanding of normal distribution, including standard deviation and z-scores

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Interpret statistical data using confidence intervals, confidence levels, and margin of error

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Confidence intervals to estimate population mean

Critically analyze society's use of inferential statistics

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Mean hypothesis testing with t-distribution

Hypothesis Testing Mean Claims without Knowing <katex> \sigma </katex>

Parent Assignments

Challenge Zone

Foundation Review

Mathematics 11

Logical Reasoning

Measurement

Relations and Functions

math

Ex. 1:

Ex. 2:

Ex. 3:

Subtracting f(x) and g(x) using points from their graphs

Subtracting f(x) minus g(x) with polynomial functions

Computing g(x) minus f(x) with polynomial expressions

Evaluating (g−f)(−2) using two different methods

Sketching g(x) minus f(x) from two graphs

Evaluating (g−f) at three points using graphs

This lesson explains how to subtract one function from another to form a new function, written as (f minus g)(x). It covers the subtraction formula, why the domain of the result is the overlap of both original domains, and walks through worked examples with polynomial and radical functions.

Adding and subtracting polynomials

Function notation

Function notation (Advanced)

Operations with functions

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Overview

Subtracting Functions

What You'll Learn

Subtracting functions means creating a new function by writing (f minus g)(x) equals f(x) minus g(x).

You subtract the two output expressions and then simplify by combining like terms.

The domain of the difference function is the set of x values shared by the domains of both original functions.

Order matters, since (f minus g)(x) is generally not the same as (g minus f)(x).

Watch for a minus sign in front of a whole expression, since it must be distributed to every term inside.

What You'll Practice

Subtracting polynomial functions with multiple terms

Evaluating function differences at specific x-values algebraically

Reading coordinates from graphs to compute function subtraction

Sketching difference graphs by plotting key points and turning points

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

6 Video lessons

Practice exercises

Learning resources

Skills

Function Operations

Function Subtraction

Polynomial Expressions

Function Evaluation

Graph Analysis

Coordinate Reading