𝐌𝐚𝐠𝐢𝐜 𝐒𝐪𝐮𝐚𝐫𝐞: 𝐀𝐏 𝐏𝐫𝐞𝐜𝐚𝐥𝐜𝐮𝐥𝐮𝐬 Unit 1 Review Name:
𝐀 𝐁 𝐂 𝐃
𝐄 𝐅 𝐆 𝐇
𝐈 𝐉 𝐊 𝐋
𝐌 𝐍 𝐎 𝐏
Directions: Circle any letter in the square above and then cross out the letters in the same row and column. Circle
another letter and cross the letters in the same row and column. Circle a third letter and cross out the letters in the same
row and column. Finally, circle the remaining letter so that you have 4 total letters circled. Answer the four problems that
correspond to the four letters you selected. Write your answers in the table at the bottom of the last page.
A. The polynomial function f is given by f ( x ) = 3x 4 − 6 x 3 + 4 x − 5. What is the degree of the polynomial?
𝑥 −1 0 3 4
𝑓(𝑥) 5 4 −1 −5
𝐁. Selected values of the function 𝑓(𝑥) are shown in the table above. Find the average rate of change of 𝑓(𝑥) over
the interval [−1, 4].
C. The figure shown above is the graph of a polynomial function g. The graph has a root with multiplicity of 2 at x = b.
What is the value of b?
𝐌𝐚𝐠𝐢𝐜 𝐒𝐪𝐮𝐚𝐫𝐞 Activity Concept - Bryan Passwater Activity by Vicki Carter
D. The polynomial function f is given by f ( x ) = ( x + 2 ) ( x 2 − 3x − 10 ) . The function has two distinct real zeros. What is
the value of the largest zero?
E. The polynomial function f is an odd function. If f ( 3) = −7 is a point on the graph of f, what is the value of f ( −3) ?
𝑥 −5 −3 −1 1
𝑓(𝑥) −14 −11 −8 −5
F. Selected values of the linear function f are shown above. Find f ( 5 ) .
G. The figure shown above is the graph of a rational function g. The graph has a horizontal asymptote of y = b. What is
the value of b?
2 x + 10
H. The rational function f is given by f ( x ) = . The function has a vertical asymptote at x = a. What is the
x − 3x − 40
2
value of a?
𝐌𝐚𝐠𝐢𝐜 𝐒𝐪𝐮𝐚𝐫𝐞 Activity Concept - Bryan Passwater Activity by Vicki Carter
I. The polynomial function p is given by p ( x ) = −5 x m + 3x 5 − 4. What is the smallest value of m that is possible if the
function p has the following characteristics?
lim p ( x ) = −
x →−
lim
x →
p ( x ) = −
𝑥 −1 0 1 2
𝑓(𝑥) −2 2 6 2
J. Selected values of a polynomial function f are shown above. Let g ( x ) = af ( x + h ) + k , where a, h, and k are
constants. In the xy-plane, the graph of g is constructed by applying three transformations to the graph of f in this
order: a horizontal translation by 3 units, a vertical dilation by a factor of 2, and a vertical translation by 4 units. What
is the value of g ( 2 ) ?
K. The graph of function k is shown above. The extrema for k are labeled and the point of inflection of the graph of k is
labeled. The function k is decreasing and the graph of k is concave down on the interval ( p, q ) .
What is the value of p?
𝐌𝐚𝐠𝐢𝐜 𝐒𝐪𝐮𝐚𝐫𝐞 Activity Concept - Bryan Passwater Activity by Vicki Carter
2 x 2 + 3x − 9
L. The rational function r is given by r ( x ) = . The slant asymptote is in the form of y = mx + b. Find the
x−2
value of b.
M. The polynomial function f is given by f ( x ) = ( x + 3) . Find the coefficient of the term containing x 2 . What is the
4
result when you divide this coefficient by 6?
𝑥 −2 −1 1 2
𝑓(𝑥) −3 −2 −1 2
N. Selected values of a polynomial function f are shown above. Let g ( x ) = af ( bx ) + k , where a, b, and c are positive
constants. In the xy-plane, the graph of g is constructed by applying three transformations to the graph of f in this
order: a horizontal dilation by a factor of 3, a vertical dilation by a factor of 2, and a vertical translation by 7 units. If
g ( m ) = 5, find the value of m.
𝐌𝐚𝐠𝐢𝐜 𝐒𝐪𝐮𝐚𝐫𝐞 Activity Concept - Bryan Passwater Activity by Vicki Carter
O. In the figure above, the graph of the polynomial function f is shown as the solid curve. The graph of g, shown as a
dotted curve, is a transformation of the graph of f, where g ( x ) = f ( x + h ) + k , where h and k are constants. Find the
value of k − h.
3x 2 − 8 x − 3
P. Let f be a rational function given by f ( x ) = . When f is graphed in the xy-plane, there is a hole in the
x2 − 5x + 6
graph. What is the y-coordinate of the hole?
𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐋𝐞𝐭𝐭𝐞𝐫 𝐀𝐧𝐬𝐰𝐞𝐫
𝐒𝐮𝐦 𝐨𝐟 𝐚𝐥𝐥 𝟒 𝐚𝐧𝐬𝐰𝐞𝐫𝐬:
𝐌𝐚𝐠𝐢𝐜 𝐒𝐪𝐮𝐚𝐫𝐞 Activity Concept - Bryan Passwater Activity by Vicki Carter
