1.1

• A function is a mathematical relation that maps a set of input values to a set of output values such that each input value is mapped to exactly one output value.
• The set of input values of a function is called the domain, represented by the independent variable.
• The set of output values of a function is called the range, represented by the dependent variable.
• The function $f$ is positive when the graph of $f$ lies above the x-axis, i.e. the outputs (y-values) are greater than zero.
• The function $f$ is negative when the graph of $f$ lies below the x-axis, i.e. the outputs (y-values) are less than zero.
• Concave up


  The rate of change is increasing.

  
• Concave down


  The rate of change is decreasing.

  
• "$f$ is increasing" refers to...


  function values
• "the rate of change of$f$ is increasing" refers to...


  concavity
• • $f$ is positive because the outputs (y-values) are all positive, i.e. the graph of $f$ lies above the x-axis.
  • $f$ is decreasing because the outputs (y-values) decrease as the inputs (x-values) increase, i.e. the graph of $f$ "goes down" as we move to the right.
  • The rate of change of $f$ is increasing because the graph of $f$ is concave up.

  
• • $g$ is negative because the outputs (y-values) are all negative, i.e. the graph of $g$ lies below the x-axis.
  • $g$ is increasing because the outputs (y-values) increase as the inputs (x-values) increase, i.e. the graph of $g$ "goes up" as we move to the right.
  • The rate of change of $g$ is decreasing because the graph of $g$ is concave down.

  
• describing rate of change

  The rate of change is increasing/decreasing because the graph of h is concave up/down on the interval ($t_1,t_2$).