Unit 1

• A relation is an identified property that connects two sets of numbers or variables.
• The range of the function is all possible values of y.
• The domain of the function is all possible values of x.
• A function is a relation where every input has only one output.
• A continuous function is a function whose graph has no jumps or gaps in it (ex. line, parabola); often the domain is any real number.
• A discrete function is a function that is defined for a set of numbers that an be 'listed'.
• A discontinuous function is a function whose graph has jumps or gaps in it.
• $g(x) =$$x^2$ is an example of a quadratic function
• $f(x) =$$x$ is an example of a linear equation
• $h(x) =$$x^3$ is an example of a cubic function
• $k(x) =$$\sqrt{x}$ is an example of a square root function
• $q(x) =$$^3\sqrt{x}$ is an example of a cubic root function
• $p(x)=$$|x|$ is an example of an absolute value function
• $r(x) =$$1/x$ is an example of a reciprocal function
• The variable d is the variable that shifts the graph left or right in a horizontal transformation.
• The variable k is the variable that compresses or stretches the graph horizontally.
• The variable c is the variable that shifts the graph up or down in a vertical transformation.
• The variable a is the variable that compresses or stretches the graph vertically.
• If d>0: the graph shifts to the right.
• If d<0: the graph shifts to the left.
• If k>1: the graph is horizontally compressed.
• If 0<k<1: the graph is horizontally stretched.
• If k<0: the graph is reflected across the y axis.
• If c>0: the graph shifts up.
• If c <0: the graph shifts down.
• If a>1: the graph is vertically stretched.
• If 0<a<1: the graph is vertically compressed.
• If a<0: the graph is reflected across the x axis.
• linear function

  
• quadratic function

  
• cubic function

  
• square root function

  
• absolute value function

  
• cubic root function

  
• reciprocal function