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(:title y-intercept:) >>nav_bar<<%reg%Mathcasts         %exa%Examples      %pra%Practice%%    %mor%More      %up%[[glossary/Y]] >><< [[<<]] ---- [table border=1 cellpadding=5 width=98%] [row] []>>&<< %def b%Definition:%% The %red b%y-intercept%% of a function is the point at which the function crosses the y-axis. >>-<< %reg b%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. >>&<< [table] [row] [] >>&<< %exa b%Example:%% Find the y-intercept of the quadratic function {$ f(x)= x^2+2x-1 $} (:div style="margin-left:20px":)>>&<>&<>&<>le20 a6<< [table border=2 bordercolor=#ddddff cellspacing=0 cellpadding=5 bgcolor=#eeeeff style='color:#000066; font-size:1em;'] [row] [c width=180] %exa c11% {$ y=-x+2 $}%% [c width=180] %pra c11% {$ y=\frac{1}{x} $}%% [c width=180] %mor c11% {$ y=2^x $}%% [c width=180] %bgr c11% {$ f(x)=\sqrt{x+3} $} [row] [c] %exa% y-intercept: 2 [c] %pra% y-intercept: none [c] %mor% y-intercept: 1 [c] %bgr% y-intercept: {$ \sqrt{3}=1.732 $} [row] [c] {gg width=160; height=200; xmin=-4; xmax=4; xscl=1; axes(); stroke="#660000"; strokewidth=2; plot("-x+2"); dot([0,2],"open"); c=text([0,2],"y-intercept",aboveright);gg} [c] {gg width=160; height=200; xmin=-4; xmax=4; xscl=1; axes(); stroke="#006600"; strokewidth=2; plot("1/x"); gg} [c] {gg width=160; height=200; xmin=-4; xmax=4; xscl=1; axes(); stroke="#660099"; strokewidth=2; plot("2^x"); dot([0,1],"open"); c=text([0,1],"y-intercept",belowright); gg} [c] {gg width=160; height=200; xmin=-4; xmax=4; xscl=1; axes(); stroke="#009999"; strokewidth=2; plot("sqrt(x+3)"); dot([0,1.732],"open"); c=text([0,1.732],"y-intercept",belowright); gg} [tableend] [tableend] >>&<< ------------- >>&<< %rel%Related topics: * [[function]] * [[root]] of a function (x-intercepts) * [[linear function]] * [[quadratic function]] >>&<< ---- (:showhide3 init=hide div=box4 lshow='Add comment' lhide='Close':) >>id=box4<< (:commentbox:) >><< [table width=100%] [row] [][[glossary/Y| Attach:main/tri_purple_up_a.gif ]] [[glossary/Y| Up one level]] [r](:html:) (:htmlend:) [tableend]