F(n)=4−2n{\displaystyle F(n)=4-2n} y=3t−120{\displaystyle y=3t-120} F(x)=23x+3{\displaystyle F(x)={\frac {2}{3}}x+3}
If the slope is negative, that means the line goes down as you move to the right.
If the slope is negative, that means the line goes down as you move to the right.
-1: -1 + 2 = 1 0: 0 +2 = 2 1: 1 + 2 = 3
Quadratic functions Rational functions Logarithmic functions Graphing inequalities (not functions, but still useful information).
F(x)=2x2−18{\displaystyle F(x)=2x^{2}-18} Set F(x) equal to zero: 0=2x2−18{\displaystyle 0=2x^{2}-18} Solve: 0=2x2−18{\displaystyle 0=2x^{2}-18} 18=2x2{\displaystyle 18=2x^{2}} 9=x2{\displaystyle 9=x^{2}} x=3,−3{\displaystyle x=3,-3}[11] X Research source
18=2x2{\displaystyle 18=2x^{2}} 9=x2{\displaystyle 9=x^{2}} x=3,−3{\displaystyle x=3,-3}[11] X Research source
Some squared functions, like F(n)=n2{\displaystyle F(n)=n^{2}} can never be negative. Thus there is an asymptote at 0. Unless you’re working with imaginary numbers, you cannot have −1{\displaystyle {\sqrt {-1}}}[12] X Research source For equations with complex exponents, you may have many asymptotes.
For the equation y=5x2+6{\displaystyle y=5x^{2}+6}, you might plug in -1,0,1, -2, 2, -10, and 10. This gives you a nice range of numbers to compare. Be smart selecting numbers. In the example, you’ll quickly realize that having a negative sign doesn’t matter – you can stop testing -10, for example, because it will be the same as 10.
Plug in 2-4 large values of x, half negative and half positive, and plot the points. What happens if you plugged in “infinity” for one variable? Does the function get infinitely bigger or smaller? If the degrees are the same in a fraction, like F(x)=x3−2x3+4{\displaystyle F(x)={\frac {x^{3}}{-2x^{3}+4}}}, simply divide the first two coefficients (1−2{\displaystyle {\frac {1}{-2}}} to get your ending asymptote (-. 5). [14] X Research source If the degrees are different in a fraction, you must divide the equation in the numerator by the equation in denominator by Polynomial Long Division.
