John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Unlocking the Power of Linear Equations with the Linear Parent Function.

Linear parent function f(x)=xDomain: {x| -∞ < x < ∞}Range: {y| -∞ < y < ∞}x & y intercept: (0,0)Max # of roots/zeros: 1Continuous The linear parent...

John Rhodes
June 21, 2023
Calculus

Understanding the Absolute Value Parent Function and its Transformations in Algebra

Absolute value parent function f(x)=|x|Domain: {x| -∞ < x < ∞}Range: {y| ∞ < y < ∞}x & y intercept: (0,0)Max # of roots/zeros: 2Continuous The absolute...

John Rhodes
June 21, 2023
Calculus

Using the Intermediate Value Theorem to Determine the Existence of a Zero Crossing in a Continuous Function over an Interval

If f(1)4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis. Intermediate Value Theorem We cannot make that conclusion...

John Rhodes
June 21, 2023
Calculus

Understanding Slope of Secant Line and Instantaneous Rate of Change in Math

Slope of secant line between two points, use to estimate instantanous rate of change at a point. Average Rate of Change The slope of a secant line...

John Rhodes
June 21, 2023
Calculus

How to Find the Slope of a Tangent Line Using Calculus: A Step-By-Step Guide

Slope of tangent line at a point, value of derivative at a point Instantenous Rate of Change When we have a function f(x), the derivative at a...

John Rhodes
June 21, 2023
Calculus

Understanding the First Principle of Differentiation: Finding the Derivative of a Function

limit as h approaches 0 of [f(x+h)-f(x)]/h Formal definition of derivative The expression [f(x+h) – f(x)]/h represents the slope of the line passing through the points (x,...

John Rhodes
June 21, 2023
Calculus

The Definition of Derivative in Mathematics – Understanding Instantaneous Rates of Change and Tangent Lines

limit as x approaches a of [f(x)-f(a)]/(x-a) Alternate definition of derivative This is the formula for the definition of the derivative of a function f(x) at a...

John Rhodes
June 21, 2023
Calculus

Understanding and Addressing Decreasing Trends in Numerical Data: Strategies for Analysis and Improvement

decreasing When f ‘(x) is negative, f(x) is Decreasing refers to a trend or pattern where something is becoming less in quantity, size, or intensity over time....