Definition: The y-intercept of a function is the point at which the function crosses the y-axis.

Rules:

  • The y-axis is also the line x=0. So substituting x=0 into the function gives the y-intercept.
  • by definition, a function is single-valued. This means that a function can have at most one y-intercept.

Example: Find the y-intercept of the quadratic function f(x)= x^2+2x-1

Substitute x=0 into the function: f(0)=3 \cdot 0^2+2 \cdot 0-1 =-1
So the y-intercept is: -1 .
That is, the point where this function crosses the y-axis is: (0,-1).

  
y=-x+2 y=\frac{1}{x} y=2^x f(x)=\sqrt{x+3}
y-intercept: 2 y-intercept: none y-intercept: 1 y-intercept: \sqrt{3}=1.732

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Page last modified on March 14, 2008, at 04:46 AM