how do you determine the intercepts from an equation or graph???

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how do you determine the intercepts from an equation or graph???

Mathematics
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for the Y- intercept, you replace all the x's for zeroes, because any y-intercept has coordinates of (0,k) where "k" is a real number, for instance: \[f:f(x)=e^x-u\] This function will have a Y-intercept of "1-k" because by definition, you fin the Y-intercept by replacing all the x's for zero, in other words "f(0)": \[f: f(0)=e^0-u\] \[f:f(0)=1-u\] So, we conclude that the function f intersects the y-axis on the point (0,1-u). For the x-interception it's a little more complex, but easy as well, because it's pretty much the opposite of the y-interception, the x-interception points are often called "roots" or "zeroes" of the function. So, by definition a root point must have coordinates (k,0) where "k" is a real number, let's take for example: \[g:g(x)=3x-9\] In order to find the roots of this function we look for the values for "x" that make the whole function g equal zero, meaning "g(x)=0": \[3x-9=0\] And we solve for "x": \[x=\frac{ 9 }{ 3 }\] \[x=3\] So, now we have found that the function g has it's x-interception on the coordinates (3,0).
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