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

• Determine the equations of the inverses of the functions:
  • [latex]\scriptsize y=ax+q[/latex]
  • [latex]\scriptsize y=a{{x}^{2}}[/latex]
  • [latex]\scriptsize y={{a}^{x}},a \gt 0[/latex] ([latex]\scriptsize y={{a}^{x}}[/latex] may be left with [latex]\scriptsize x[/latex] as the subject of the formula. Note: No logarithms required.)
• Sketch the graphs of the inverse of the functions:
  • [latex]\scriptsize y=ax+q[/latex]
  • [latex]\scriptsize y=a{{x}^{2}}[/latex]
  • [latex]\scriptsize y={{a}^{x}},a \gt 0[/latex]
    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:
  • [latex]\scriptsize y=ax+q[/latex]
  • [latex]\scriptsize y=a{{x}^{2}}[/latex]
  • [latex]\scriptsize y={{a}^{x}},a \gt 0[/latex]
• Identify characteristics as listed below with respect to the following functions and their inverses:
  [latex]\scriptsize y=ax+q[/latex]
  [latex]\scriptsize y=a{{x}^{2}}[/latex]
  [latex]\scriptsize y={{a}^{x}},a \gt 0[/latex]
  • 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.

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

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

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

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

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

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