# Reciprocal Functions

These techniques involves sketching the graph of $y=\dfrac{1}{f(x)}$ from the graph of $y=f(x)$.

## Technique 1

When $f(x)$ approaches towards $0$, $y=\dfrac{1}{f(x)}$ approaches towards $\infty$, the graph of $y=\dfrac{1}{f(x)}$ approaches the vertical asymptote(s).

## Technique 2

The graph of $y=\dfrac{1}{f(x)}$ has vertical asymptotes at the $x$-intercepts of $y=f(x)$.

## Technique 3

When $f(x)$ approaches towards $\infty$, $y=\dfrac{1}{f(x)}$ approaches towards $0$, the graph of $y=\dfrac{1}{f(x)}$ approaches the horizontal asymptote(s).

## Technique 4

- When $f(x)=\pm1$, $\dfrac{1}{f(x)}=\pm1$. The graphs are in the same quadrant.
- When $f(x) \lt 0$, $\dfrac{1}{f(x)} \lt 0$.
- When $f(x) \gt 0$, $\dfrac{1}{f(x)} \gt 0$.

## Technique 5

- The minimum turning point of $f(x)$ gives the maximum turning point of the reciprocal function.
- The maximum turning point of $f(x)$ gives the minimum turning point of the reciprocal function.

### Example 1

Draw the reciprocal graph of the following function.

### Example 2

Draw the reciprocal graph of the following function.

### Example 3

Draw the reciprocal graph of the following function.

### Example 4

Draw the reciprocal graph of the following function.

### Example 5

Draw the reciprocal graph of the following function.

**✓ **Unlock your full learning potential—download our expertly crafted slide files for free and transform your self-study sessions!

**✓ **Discover more enlightening videos by visiting our YouTube channel!

Algebra Algebraic Fractions Arc Binomial Expansion Capacity Common Difference Common Ratio Differentiation Double-Angle Formula Equation Exponent Exponential Function Factorise Functions Geometric Sequence Geometric Series Index Laws Inequality Integration Kinematics Length Conversion Logarithm Logarithmic Functions Mass Conversion Mathematical Induction Measurement Perfect Square Perimeter Prime Factorisation Probability Product Rule Proof Pythagoras Theorem Quadratic Quadratic Factorise Ratio Rational Functions Sequence Sketching Graphs Surds Time Transformation Trigonometric Functions Trigonometric Properties Volume

## Responses