# Functions and algebra: Use a variety of techniques to sketch and interpret information for graphs of the inverse of a function

### Subject outcome

Subject outcome 2.2: Use a variety of techniques to sketch and interpret information for graphs of the inverse of a function theorems

### Learning outcomes

• Determine the equations of the inverses of the functions:
• $\scriptsize y=ax+q$
• $\scriptsize y=a{{x}^{2}}$
• $\scriptsize y={{a}^{x}},a \gt 0$ ($\scriptsize y={{a}^{x}}$ may be left with $\scriptsize x$ as the subject of the formula. Note: No logarithms required.)
• Sketch the graphs of the inverse of the functions:
• $\scriptsize y=ax+q$
• $\scriptsize y=a{{x}^{2}}$
• $\scriptsize y={{a}^{x}},a \gt 0$
Note: Sketching the graphs using point by point plotting is an option.
• Obtain the equation of any of the following inverse graphs given as a sketch:
• $\scriptsize y=ax+q$
• $\scriptsize y=a{{x}^{2}}$
• $\scriptsize y={{a}^{x}},a \gt 0$
• Identify characteristics as listed below with respect to the following functions and their inverses:
$\scriptsize y=ax+q$
$\scriptsize y=a{{x}^{2}}$
$\scriptsize y={{a}^{x}},a \gt 0$

• Domain and range
• Intercepts with axes
• Turning points, minima and maxima
• Asymptotes
• Shape and symmetry
• Functions or non-functions
• Continuous or discontinuous
• Intervals in which a function increases/decreases.

### Unit 1 outcomes

By the end of this unit you will be able to:

• Define an inverse function.
• Find the inverse of $\scriptsize y=ax+q$.
• Sketch the inverse of $\scriptsize y=ax+q$.
• Answer questions about the domain, range, shape, continuity and other characteristics of the inverse graph.

### Unit 2 outcomes

By the end of this unit you will be able to:

• Find the inverse of $\scriptsize y=a{{x}^{2}}$.
• Sketch the inverse of $\scriptsize y=a{{x}^{2}}$.
• Answer questions about the domain, range, shape, continuity and other characteristics of the inverse graph.

### Unit 3 outcomes

By the end of this unit you will be able to:

• Find the inverse of $\scriptsize y={{a}^{x}}$ where $\scriptsize a \gt 0$.
• Sketch the inverse of $\scriptsize y={{a}^{x}}$ where $\scriptsize a \gt 0$.
• Answer questions about the domain, range, shape, continuity and other characteristics of the inverse graph.