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descrube hiw to determine the intercepts of arational function​

Sagot :

UnknorM0usidn

Describe how to determine the intercepts of rational function?

[tex]\large \: \: \: \: \: \: ➢[/tex]To find the intercepts replace 0 for x and solve y of x after that. To find the intercepts the point where the graph crosses the x-axis "also known as zeros, substitute 0 for y and solve for x.

Example:

[tex]\large \: ➢[/tex]Find the intercepts of the function given.

[tex] \: \: \: \: \: \: \large\tt f(x) = \frac{ \: \: x + 10 \: \: }{x - 5} [/tex]

[tex]\large \: ➢[/tex]To find the y-intercept, we must substitute in 0 for each x:

[tex] \: \: \: \: \: \: \large \tt \: f(x) = \frac{ \: \: 0 + 10 \: \: }{0 - 5} [/tex]

[tex]\large \: ➢[/tex]And then simplify:

[tex] \: \: \: \: \: \: \large \tt f(x) = \frac{ \: \: 10 \: \: }{ - 5} [/tex]

[tex]\: \: \: \: \: \: \large \tt f(x) = \: - 2[/tex]

[tex]\large \: ➢[/tex]There is a y-intercept at ( 0.2 ). (Notice that 0 is the x coordinate because on the y-axis, x = 0.)

[tex]\large \: ➢[/tex]To find the x-intercept, we must substitute in 0 for y or f(x):

[tex] \: \: \: \: \: \: \large \tt 0 = \frac{ \: \: x + 10 \: \: }{x - 5} [/tex]

[tex] \: \: \: \: \: \: \large \tt0(x - 5) = x + 10[/tex]

[tex] \: \: \: \: \: \: \large \tt0 = x + 10[/tex]

[tex] \: \: \: \: \: \: \large \tt x = - 10[/tex]

[tex]\large \: ➢[/tex]There is a y-intercept at ( -10,0 ). (Notice that 0 is the y coordinate because on the x-axis, y = 0.)

Note:

[tex]\large \: ➢[/tex]Not all rational functions have both an x or y intercept. If you cannot find a real solution, then it does not have that intercept.

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