y-intercept

If the y-axis goes through the coordinate origin (0 | 0), then the y-axis intercept , ordinate intercept or reference point designates the - coordinate of the intersection of a function graph with the y-axis or ordinate . Regardless of the position of the y-axis, the y-axis intercept always corresponds to the function value at the point . ${\displaystyle y}$ ${\displaystyle x=0}$

y-intercepts of some functions

• In the case of linear functions, that is , the absolute (= constant) term of the function term indicates the y-axis intercept. Example :; the y-intercept is 7. A special case of this is: ${\displaystyle f(x)=mx+b}$ ${\displaystyle f(x)=3\cdot x+7}$
• In the case of homogeneous linear (proportional) functions, i.e. whose graph runs through the origin of the coordinate system, the y-axis intercept is therefore 0. ${\displaystyle f(x)=mx}$
• Is the y-intercept of the linear function whose graph passes through points and ${\displaystyle (x_{1},y_{1})}$ ${\displaystyle (x_{2},y_{2})}$

  ${\displaystyle q=y_{1}-{\frac {y_{1}-y_{2}}{x_{1}-x_{2}}}x_{1}={\frac {x_{1}\cdot y_{2}-x_{2}\cdot y_{1}}{x_{1}-x_{2}}}.}$

• For all power functions with the y-axis intercept is 0. ${\displaystyle f(x)=ax^{r}}$ ${\displaystyle r>0}$
• Even with quadratic functions (whose graph is a parabola) the absolute term (= constant term) of the function term indicates the y-axis intercept. ${\displaystyle c}$ ${\displaystyle f(x)=ax^{2}+bx+c}$
• In general, this applies to all completely rational functions, i.e. for all functions whose function term is a polynomial. If the function term has the form , the absolute term indicates the y-axis intercept of the function graph. ${\displaystyle f(x)=a_{n}x^{n}+\dots +a_{1}x+a_{0}}$ ${\displaystyle a_{0}}$

• For exponential functions whose function term has the form , the function graph has the y-axis intercept . In particular, the y-axis intercept is equal to 1 for functions of the shape . ${\displaystyle f(x)=ca^{x}}$ ${\displaystyle c}$ ${\displaystyle f(x)=a^{x}}$

See also

• Zero of a function
• Intercept shape of lines and planes

Remarks

1. ↑ DMV: "First Aid: The Linear Function"