Ch. 3 Key Equations – College Algebra 2e | OpenStax
Key Equations
| Constant function | [latex]f(x)=c,[/latex] where [latex]c[/latex] is a constant |
| Identity function | [latex]f(x)=x[/latex] |
| Absolute value function | [latex]f(x)=|x|[/latex] |
| Quadratic function | [latex]f(x)=x^2[/latex] |
| Cubic function | [latex]f(x)=x^3[/latex] |
| Reciprocal function | [latex]f(x)=\frac{1}{x}[/latex] |
| Reciprocal squared function | [latex]f(x)=\frac{1}{x^2}[/latex] |
| Square root function | [latex]f(x)=\sqrt{x}[/latex] |
| Cube root function | [latex]f(x)=\sqrt[3]{x}[/latex] |
| Average rate of change | [latex]\frac{\Delta y}{\Delta x}=\frac{f(x_2)=f(x_1)}{x_2-x_1}[/latex] |
| Composite function | [latex](f\circ g)(x)=f(g(x))[/latex] |
| Vertical shift | [latex]g(x)=f(x)+k[/latex] (up for [latex]k>0[/latex]) |
| Horizontal shift | [latex]g(x)=f(x-h)[/latex] (right for [latex]h>0[/latex]) |
| Vertical reflection | [latex]g(x)=-f(x)[/latex] |
| Horizontal reflection | [latex]g(x)=f(-x)[/latex] |
| Vertical stretch | [latex]g(x)=af(x)\hspace{0.5em}(a>0)[/latex] |
| Vertical compression | [latex]g(x)=af(x)\hspace{0.5em}(0< a< 1)[/latex] |
| Horizontal stretch | [latex]g(x)=f(bx)\hspace{0.5em}(0< b< 1)[/latex] |
| Horizontal compression. | [latex]g(x)=f(bx)\hspace{0.5em}(b> 1)[/latex] |
