1 of 25
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.

x2 – 4x
16; x2 – 4x + 16 = (x – 4)2
-4; x2 – 4x – 4 = (x – 2)2
-16; x2 – 4x – 16 = (x – 4)2
4; x2 – 4x + 4 = (x – 2)2

2 of 25
Determine whether the equation defines y as a function of x.

xy + 5y = 1
y is a function of x
y is not a function of x

3 of 25
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.

f(x) = 7 – x4
origin symmetry
y-axis symmetry
neither

4 of 25
Evaluate or simplify the expression without using a calculator.

log 0.0001
14
-14
-4
4

5 of 25
Express the interval in set-builder notation and graph the interval on a number line.

6 of 25
Find a rational zero of the polynomial function and use it to find all the zeros of the function.

f(x) = 2×3 – x2 – 12x + 6
{12, 6, -6}
{-2, 6, -6}
{2, 6, -6}
{-12, 6, -6}

7 of 25
Find functions f and g so that h(x) = (f 째 g)(x).

h(x) = (59×2 + 78)
f(x) = 59×2 + 78, g(x) = x
f(x) = x, g(x) = 59×2 + 78
f(x) = (59×2), g(x) = 78
f(x) = (59x + 78), g(x) = x2

8 of 25
Find the domain of the composite function f 째 g.

f(x) =2x+10, g(x) =60x

(-, , -10) or (-10, 0) or (0, , 0) or (0, -6) or (-6, , -10) or (-10, -6) or (-6, 0) or (0, )

9 of 25
Find the inverse of the one-to-one function.

f-1(x) = x3 + 6
f-1(x) = x + 6
f-1(x) =1×3+6
f-1(x) = x3 + 36

10 of 25
Find the product.

(9x – 8)2
81×2 + 64
9×2 + 64
9×2 – 144x + 64
81×2 – 144x + 64

11 of 25
Find the product.

( 10 + 7x)2
100 + 140x + 49×2
100 + 49×2
100 + 140x + 7×2
100×2 + 140x + 49

12 of 25
Find the product.

(x – 4y)( 5x – 9y)
5×2 – 29xy – 29y2
x2 – 29xy + 36y2
x2 – 29xy – 29y2
5×2 – 29xy + 36y2

13 of 25
Graph the function by making a table of coordinates.

f(x) = 4x

14 of 25
Graph the rational function.

15 of 25
Multiply or divide as indicated.

x-3x+2
x+2x-3
x-2x+3
x+2x+3

16 of 25
Perform the indicated operations.

( 9×4 + 3xy – y3) – (x4 + 7xy + 3y3)
9×4 – 4xy – 4y3
10×4 + 12xy + 2y3
8×4 – 4xy – 4y3
8×4 – 4xy – 2y3

17 of 25
Perform the indicated operations. Write the resulting polynomial in standard form.

(-5×6 – 13×5 – 19) + (3×6 + 9×5 + 3)
-2×6 – 4×5 – 16
-2×6 + 14×5 + 22
-22×11
-2×6 – 4×5 + 22

18 of 25
Simplify the exponential expression.

x9y0

1A?9
1
x9
0

19 of 25
Solve the absolute value inequality. Other than A~, use interval notation to express the solution set and graph the solution set on a number line.

20 of 25
Solve the formula for the specified variable.d = rt for t
t =rd
t = d – r
t = d r
t =dr

21 of 25
The equation V = -2000t + 20,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $ 12,000, substitute 12,000 into the equation to find the age of the car.
5 years
4 years
3 years
6 years

22 of 25
Use interval notation to represent all values of x satisfying the given conditions.

y1 = 6x – 6, y2 = 5x – 4, and y1 y2.
[ -10, )
[ 2, , 2]
(- 2)

23 of 25
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.

16(log2x + log2y) – 2 log2 (x + 9)

24 of 25
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.

x3 + 2×2 – 11x – 12 = 0; -4
{ 3, 1, -4}
{ 3, -1, -4}
{ -3, 1, -4}
{ -3, -1, -4}

25 of 25
Use the graph of the given function to find any relative maxima and relative minima.

f(x) = x3 – 3×2 + 1

maximum: none; minimum: (2, -3)
no maximum or minimum
maximum: (0, 1); minimum: none
maximum: (0, 1); minimum: (2, -3)