Rationals online Formative Quiz Fall 2020 Q1 (1)
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Millwoods Christian School *
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CALCULUS
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Mathematics
Date
Nov 24, 2024
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docx
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Formative Quiz – Rational Functions Name:_______________________ Mark /14 Use the information below to answer the two questions below The graph below is a transformation of the graph of =
��
1
��
. The equations of the asymptotes are x=2 and y=4 and the points marked with solid dots are (3, 1) and (5, 3). The equation of the graph can be written in the form =
��
��
−ℎ
��
+ ��
. 1. The value of ��
is _____ 2. The value of ��
is A. 3 B. -3 C. 1
3 D. −
1
3
The graph of the rational function shown has two asymptotes and a point of
discontinuity. 4. The equation of this graph is 2 x x f x 2 11 12 ( ) = 6. The zeros(s) of the function − + x A. 3
2 B. 4 C. -3 D. 3
2
and 4
−
is/are
4 Use the following information to answer the next three questions. x − 7 A student graphed the function f x and he determined the equation of the ( ) = 2 x x − + 11 28 asymptotes and the coordinates of the point of discontinuity. A list of possible equations for the asymptotes are listed below. Equation 1 x = 7 Equation 5 y = 0 Equation 2 x = -7 Equation 6 y = 1 Equation 3 x = 4 Equation 7 y = 4 Equation 4 x = -4 Equation 8 y = -4 7. The equation of the horizontal asymptote on the graph of y = f(x) is equation number ______. 8. The equation of the vertical asymptote on the graph of y = f(x) is equation number _______. 9. On the graph of y = f(x)
, if the point of discontinuity is at the coordinate (
a
, b
), then the value of b
, to the nearest tenth, is _________.
Use the following information to answer the next two questions. A student graphed the following functions, where a, and
b are natural numbers. x a
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2 x b + f x + = ( )( ) x a x b + + ( ) 2 x b + k x ( ) = ( ) 2 2 x a − g x = x a − h x ( ) = x b − 2 x a + 10. Which function above does not have a horizontal asymptote? A.
y = f(x) B. y = g(x) C. y = h(x) D. y = k(x) 11. Which two functions above have graphs with no x-intercept? A.
y = f(x) and y = g(x) B. y = g(x) and y = h(x) C. y = f(x) and y = k(x) D. y = h(x) and y = k(x) 12. The range of the rational function (
) + 7 =
�� ��
−3
(
−1)
��
2
is A. {
|
> −7, } �� ��
������
B. {
|
< −7, } �� ��
������
C. {
|
≠ 7, } �� ��
������
D. {
|
≠ −7, } �� ��
������
13. The domain of the rational function (
) =
�� ��
��
2
��
2
+1
is A. {
|
≠ −1, } �� ��
������
B. {
|
≠ 1, } �� ��
������
C. {
|
≠ 1, ≠ −1 } �� ��
��
������
D. {
| }
�� ������
Questions 14 and 16 are BONUS questions
Hint – 14 is easier to see on a graphing calculator or by changing equation to the other format. 14. The graph of the function =
��
1
��
was transformed and when the resulting equation is rearranged, it can be written in the form (
) =
�� ��
5
+3
��
+2
��
. Which of the following is a transformation that did NOT occur? A A reflection about the x-axis B. A shift of 2 units left C. A horizontal stretch by a factor of 7 about the y-axis C. A shift of 5 units up 15. For the function (
) =
�� ��
1
−2
��
+ 6
, if the intercepts are rounded to the nearest tenth, the x-intercept can be written as = . ��
�� ��
and the y-intercept can be written as = . ��
�� ��
The values of a, b, c, and d, in that order are ___ ___ ___ ___ (do not enter any spaces or commas)
Hint, point (2, -1) is marked on the graph to help you