Learning OutcomesVerify a function using the vertical line testVerify a one-to-one function with the horizontal line testIdentify the graphs of the toolkit functionsAs we have seen in examples above, we can represent a function using a graph. Graphs display many input-output pairs in a small space....
The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular [latex]x[/latex] value. The [latex]y[/latex] value of a point where a vertical line intersects a graph represents an output for that input [latex]x[/latex] v...
How To: Given a graph, use the vertical line test to determine if the graph represents a function. Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function...
Try ItDoes the graph below represent a function?...
The Horizontal Line TestOnce we have determined that a graph defines a function, an easy way to determine if it is a one-to-one function is to use the horizontal line test. Draw horizontal lines through the graph. A horizontal line includes all points with a particular [latex]y[/latex] value...
Are either of the functions one-to-one?Identifying Basic Toolkit FunctionsIn this text we explore functions—the shapes of their graphs, their unique characteristics, their algebraic formulas, and how to solve problems with them. When learning to read, we start with the alphabet. When learning to...
Identity[latex]f\left(x\right)=x[/latex]...
Absolute value[latex]f\left(x\right)=|x|[/latex]...
Quadratic[latex]f\left(x\right)={x}^{2}[/latex]...
Cubic[latex]f\left(x\right)={x}^{3}[/latex]...
Reciprocal/ Rational[latex]f\left(x\right)=\frac{1}{x}[/latex]...
Reciprocal / Rational squared[latex]f\left(x\right)=\frac{1}{{x}^{2}}[/latex]...
Square root[latex]f\left(x\right)=\sqrt{x}[/latex]...
Cube root[latex]f\left(x\right)=\sqrt[3]{x}[/latex]...
Try ItTry ItIn this exercise, you will graph the toolkit functions using an online graphing tool. Graph each toolkit function using function notation. Make a table of values that references the function and includes at least the interval [-5,5]...