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

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Graphs of Reciprocal Functions

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What is the general form of a reciprocal function?

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

What type of graph does a reciprocal function produce?

A rectangular hyperbola

Where is the vertical asymptote for $f(x) = \frac{k}{x}$ ?

At $x = 0$

Why does $f(x) = \frac{k}{x}$ have a vertical asymptote at $x = 0$ ?

Division by zero is undefined

Where is the horizontal asymptote for $f(x) = \frac{k}{x}$ ?

At $f(x) = 0$

If $k > 0$ in $f(x) = \frac{k}{x}$ , in which quadrants do the curves lie?

Quadrants 1 and 3

If $k < 0$ in $f(x) = \frac{k}{x}$ , in which quadrants do the curves lie?

Quadrants 2 and 4

What effect does a larger $|k|$ have on the hyperbola $f(x) = \frac{k}{x}$ ?

Stretches curves away from the origin

For $f(x) = \frac{k}{x}$ with $k > 0$ , how does $f(x)$ approach 0 as $x \to \infty$ ?

From the positive side

For $f(x) = \frac{k}{x}$ with $k < 0$ , how does $f(x)$ approach 0 as $x \to -\infty$ ?

From the positive side

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

Practise the questions

What is the general form of a reciprocal function?

What type of graph does a reciprocal function produce?

Where is the vertical asymptote for f(x)=kxf(x) = \frac{k}{x}f(x)=xk​?

Why does f(x)=kxf(x) = \frac{k}{x}f(x)=xk​ have a vertical asymptote at x=0x = 0x=0?

Where is the horizontal asymptote for f(x)=kxf(x) = \frac{k}{x}f(x)=xk​?

If k>0k > 0k>0 in f(x)=kxf(x) = \frac{k}{x}f(x)=xk​, in which quadrants do the curves lie?

If k<0k < 0k<0 in f(x)=kxf(x) = \frac{k}{x}f(x)=xk​, in which quadrants do the curves lie?

What effect does a larger ∣k∣|k|∣k∣ have on the hyperbola f(x)=kxf(x) = \frac{k}{x}f(x)=xk​?

For f(x)=kxf(x) = \frac{k}{x}f(x)=xk​ with k>0k > 0k>0, how does f(x)f(x)f(x) approach 0 as x→∞x \to \inftyx→∞?

For f(x)=kxf(x) = \frac{k}{x}f(x)=xk​ with k<0k < 0k<0, how does f(x)f(x)f(x) approach 0 as x→−∞x \to -\inftyx→−∞?

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Algebraic Techniques

Solve Equations

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Trigonometric Identities and Equations

Probability

Data

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Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

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Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Where is the vertical asymptote for $f(x) = \frac{k}{x}$ ?

Why does $f(x) = \frac{k}{x}$ have a vertical asymptote at $x = 0$ ?

Where is the horizontal asymptote for $f(x) = \frac{k}{x}$ ?

If $k > 0$ in $f(x) = \frac{k}{x}$ , in which quadrants do the curves lie?

If $k < 0$ in $f(x) = \frac{k}{x}$ , in which quadrants do the curves lie?

What effect does a larger $|k|$ have on the hyperbola $f(x) = \frac{k}{x}$ ?

For $f(x) = \frac{k}{x}$ with $k > 0$ , how does $f(x)$ approach 0 as $x \to \infty$ ?

For $f(x) = \frac{k}{x}$ with $k < 0$ , how does $f(x)$ approach 0 as $x \to -\infty$ ?