How to Find Intercepts in Radical Functions

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Finding the intercepts of a function is a key first step to many complex operations in various fields of mathematics, from trigonometry to algebra to calculus. The intercepts, those points on the graph where the function crosses either the x-axis or the y-axis, can be found by calculating the zero point of the two variables (X and Y). Radical functions add a twist to the standard procedure, however, since negative numbers within a radical yield nonreal solutions, which generally leads to defined portions of the function not existing.

  • Plug in zero (0) for the value of X in the equation that defines the function and solve for Y to find the X-intercept. For the simplest radical function Y=X^(1/2), plugging in zero yields a result of zero.

  • Plug in zero for Y to find the Y-intercept. For the simplest radical function Y=X^(1/2), the answer will be zero (because the square root of zero is zero).

  • Solve for the remaining variable after you've substituted zero for the other, using algebraic manipulation in more complicated equations. Thus, to find the X-intercept for the equation defined by Y=(X+4)^(1/2), after plugging in zero for X and finding Y=(0+4)^(1/2), solve to 4^(1/2)=2.

  • Be prepared for cases when an intercept does not exist. Any time you're left with a negative number inside the radical, the solution does not exist. For example, when you substitute zero for X in Y=(X-4)^(1/2), you're left with (-4)^(1/2). Therefore, the X-intercept doesn't exist. In other words, there's no point on the graph at which the function crosses the x-axis. If you graph this function, you'll find that to be true.

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