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Graphs of Reciprocal Functions (HSC SSCE Mathematics Advanced): Flashcards

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Graphs of Reciprocal Functions

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Form of reciprocal function

$f(x) = \frac{k}{x}$ where $k \neq 0$

Name of graph for $f(x) = \frac{k}{x}$

Rectangular hyperbola

Vertical asymptote of $f(x) = \frac{k}{x}$

$x = 0$

Horizontal asymptote of $f(x) = \frac{k}{x}$

$f(x) = 0$

Quadrants for $f(x) = \frac{k}{x}$ when $k > 0$

Quadrants 1 and 3

Quadrants for $f(x) = \frac{k}{x}$ when $k < 0$

Quadrants 2 and 4

Effect of larger $|k|$ on $f(x) = \frac{k}{x}$

Curves wider, further from axes

As $x \to \infty$ for $f(x) = \frac{k}{x}$ with $k > 0$

$f(x) \to 0$ from positive side

As $x \to -\infty$ for $f(x) = \frac{k}{x}$ with $k > 0$

$f(x) \to 0$ from negative side

Why $f(x) = \frac{k}{x}$ undefined at $x = 0$ ?

Division by zero is undefined

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Graphs of Reciprocal Functions (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

Form of reciprocal function

Name of graph for f(x)=kxf(x) = \frac{k}{x}f(x)=xk​

Vertical asymptote of f(x)=kxf(x) = \frac{k}{x}f(x)=xk​

Horizontal asymptote of f(x)=kxf(x) = \frac{k}{x}f(x)=xk​

Quadrants for f(x)=kxf(x) = \frac{k}{x}f(x)=xk​ when k>0k > 0k>0

Quadrants for f(x)=kxf(x) = \frac{k}{x}f(x)=xk​ when k<0k < 0k<0

Effect of larger ∣k∣|k|∣k∣ on f(x)=kxf(x) = \frac{k}{x}f(x)=xk​

As x→∞x \to \inftyx→∞ for f(x)=kxf(x) = \frac{k}{x}f(x)=xk​ with k>0k > 0k>0

As x→−∞x \to -\inftyx→−∞ for f(x)=kxf(x) = \frac{k}{x}f(x)=xk​ with k>0k > 0k>0

Why f(x)=kxf(x) = \frac{k}{x}f(x)=xk​ undefined at x=0x = 0x=0?

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Algebraic Techniques

Solve Equations

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Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

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Exponential Functions

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Transformations

Trigonometric Identities and Equations

Probability

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Exponential Functions

Logarithmic Functions

Transformations

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Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

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Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Name of graph for $f(x) = \frac{k}{x}$

Vertical asymptote of $f(x) = \frac{k}{x}$

Horizontal asymptote of $f(x) = \frac{k}{x}$

Quadrants for $f(x) = \frac{k}{x}$ when $k > 0$

Quadrants for $f(x) = \frac{k}{x}$ when $k < 0$

Effect of larger $|k|$ on $f(x) = \frac{k}{x}$

As $x \to \infty$ for $f(x) = \frac{k}{x}$ with $k > 0$

As $x \to -\infty$ for $f(x) = \frac{k}{x}$ with $k > 0$

Why $f(x) = \frac{k}{x}$ undefined at $x = 0$ ?