1.8. Zeroes and Intercepts of Functions http://www.ck12.org
Example C
Identify the intercepts and zeroes of the function:f(x) = 1001 (x− 3 )^3 (x+ 2 )^2.
Solution:
To find they-intercept, substitute 0 forx:
y= 1001 ( 0 − 3 )^3 ( 0 + 2 )^2 = 1001 (− 27 )( 4 ) =−^108100 =− 1. 08
To find thex-intercepts, substitute 0 fory:
0 = 1001 (x− 3 )^3 (x+ 2 )^2
x= 3 ,− 2
Thus they-intercept is (0, -1.08) and thex-intercepts are (3, 0) and (-2, 0).
Concept Problem Revisited
Graphically the function has zeroes at -2 and 3 with ayintercept at about -1.1. The algebraic solution is demonstrated
in Example C.
Vocabulary
Zeroes, roots, solutionsandx-interceptsare synonyms for the points where a function crosses thexaxis.
Ay-interceptis the point where a function crosses theyaxis.
Note that in order for a function to pass the vertical line test, it must only have one y-intercept, but it may have
multiple x-intercepts.
Guided Practice
- Determine the zeroes andy-intercept of the following function using algebra:f(x) = (x+ 3 )^2 (x− 2 )
- Determine the roots andy-intercept of the following function using algebra or a graph:
f(x) =x^4 + 3 x^3 − 7 x^2 − 15 x+ 18 - Determine the intercepts of the following function graphically.