1. A polynomial function can have more than one y-intercepts. (True/False)2. An increasing polynomial function is always one-to-one. (True/False)3. A polynomial function of degree s can have s + 1 zeros. (True/False)4. There is a turning point between any two zeros of a polynomial function.(True/False)5. If a critical point (turning point) of a polynomial function p(x) exists,then p(x) is not one-to-one. (True/False)
Question
- A polynomial function can have more than one y-intercepts. (True/False)2. An increasing polynomial function is always one-to-one. (True/False)3. A polynomial function of degree s can have s + 1 zeros. (True/False)4. There is a turning point between any two zeros of a polynomial function.(True/False)5. If a critical point (turning point) of a polynomial function p(x) exists,then p(x) is not one-to-one. (True/False)
Solution
-
False - A polynomial function can only have one y-intercept, which is the point where the graph of the function crosses the y-axis.
-
False - An increasing polynomial function is not always one-to-one. For example, the function f(x) = x^3 is an increasing polynomial function, but it is not one-to-one because it does not pass the horizontal line test.
-
False - A polynomial function of degree s can have at most s zeros, not s + 1.
-
True - There is a turning point between any two zeros of a polynomial function. This is because a polynomial function changes direction at its zeros.
-
True - If a critical point (turning point) of a polynomial function p(x) exists, then p(x) is not one-to-one. This is because a one-to-one function has exactly one output for each input, and a turning point indicates that there are multiple outputs for a single input.
Similar Questions
The graph of a polynomial p(x) cuts the X-axis at 3 points and touches it at 2 other points. It also touches the Y-axis at 1 point. The number of zeroes of p(x) is
Consider a polynomial function 𝑓 ( 𝑥 ) = − 1 300 ( 𝑥 − 2 ) 2 ( 𝑥 − 3 ) ( 𝑥 + 1 ) 2 ( 𝑥 + 4 ) ( 𝑥 − 5 ) f(x)= 300 −1 (x−2) 2 (x−3)(x+1) 2 (x+4)(x−5). Choose the correct set of options. The function 𝑓 ( 𝑥 ) f(x) has exactly 7 turning points. The function 𝑓 ( 𝑥 ) f(x) has exactly 6 points where the slope is 0. The function 𝑓 ( 𝑥 ) f(x) is neither even nor odd function. In the interval 𝑥 ∈ ( 3 , 5 ) x∈(3,5), 𝑓 ( 𝑥 ) f(x) is increasing first and then decreasing. The function 𝑓 ( 𝑥 ) f(x) is negative when 𝑥 ∈ ( − 1 , 2 ) x∈(−1,2).
Determine the end behavior, maximum number of turning point(s), and maximum number ofintercepts of the following polynomial functions:(a) .(b) .(c) .(d)(e)(f)XAVIER SCHOOLSenior High School Standard ProgramGRADE 11 GENERAL MATHEMATICSSecond Semester, S.Y. 2023-2024x−P(x) = − x 3 + 20x 2 + x + 10P(x) = 15x 3 − 18x 2 + 4x − 8P(x) = 13x 4 − 2x 3 + 5x 2 + x − 6P(x) = (x + 1)(3 − x)(3x − 1)(4x + 1)P(x) = (2x − 1) 2 (1 − x)(5 − 3x)2P(x) = − (x − 1)(x + 3)2 (2 + 3x)3
Which of the following statements about polynomial functions is true?Question 14Answera.They are defined for all real numbers.b.They always have a finite number of solutions.c.They can have terms with negative powers.d.They can have fractional exponents.
The graph of a polynomial P(x) is as shown. The number of zeroes is/are
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.