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Tangent Gradient at y-Intercept (HSC SSCE Mathematics Advanced): Flashcards

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Tangent Gradient at y-Intercept

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Tangent to a curve

Straight line touching curve at exactly one point

Secant to a curve

Straight line passing through two points on a curve

Y-intercept of $y = a^x$

Always at point $(0, 1)$

Why y-intercept of $y = a^x$ is always $(0, 1)$

Because $a^0 = 1$ for any positive $a$

Secant gradient formula for $y = a^x$ at $x = 0$

$m = \frac{a^h - 1}{h}$

Effect of $h$ approaching zero on secant approximation

Secant becomes better approximation of tangent

Tangent gradient at $(0,1)$ for $y = 2^x$

Less than 1

Tangent gradient at $(0,1)$ for $y = 3^x$

Greater than 1

Gradient of a line

The slope or steepness of a line

What does gradient formula measure

Vertical change divided by horizontal change

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Tangent Gradient at y-Intercept (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

Tangent to a curve

Secant to a curve

Y-intercept of y=axy = a^xy=ax

Why y-intercept of y=axy = a^xy=ax is always (0,1)(0, 1)(0,1)

Secant gradient formula for y=axy = a^xy=ax at x=0x = 0x=0

Effect of hhh approaching zero on secant approximation

Tangent gradient at (0,1)(0,1)(0,1) for y=2xy = 2^xy=2x

Tangent gradient at (0,1)(0,1)(0,1) for y=3xy = 3^xy=3x

Gradient of a line

What does gradient formula measure

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

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Trigonometric Identities and Equations

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Exponential Functions

Logarithmic Functions

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Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Y-intercept of $y = a^x$

Why y-intercept of $y = a^x$ is always $(0, 1)$

Secant gradient formula for $y = a^x$ at $x = 0$

Effect of $h$ approaching zero on secant approximation

Tangent gradient at $(0,1)$ for $y = 2^x$

Tangent gradient at $(0,1)$ for $y = 3^x$