Name ______________________________________
Midterm Review #2
Date_______________
10H Per_____________
y
1. Identify the end behavior for each of the following functions:
f x   2 x  3x  4
3
a)
4
3
b) f x   4 x  3x  10
2
2
c)
2
1
x
-4
-3
-2
-1
1
2
3
4
-1
-2
-3
2. Factor completely:
-4

b) 3x( x 2  4)  2 x 2  4
a) 4 x 3  12 x 2  x  3

c) 12 x 2  5x  2
3. Matching: Match the description of each parabola to one of the graphs:
a) Discriminant = 0
Graph 1
b) Discriminant = -9
c) Discriminant = 9
d) Tangent to the x-axis
Graph 2
e) Imaginary roots
f) Roots are real, rational and equal
g) Roots are real, irrational, and unequal
Graph 3
4. Given each of the trigonometric functions below, identify the Domain, Range, Amplitude, Frequency, Period, and
any Vertical shifts.
a) f ( x)  2 sin2 x     1
b) g x   4 tanx   3
 8 15 
,   is a point on the unit circle; find all six trig functions of angle  .
 17 17 
5. If point Q  
6. Given function f x  , identify in words the transformations to each of the following:
a. 2 f  x y 6
b. f x  4  2
c)  f 3x 
y
8
8
7. Given the graph
of f(x) for each of the following, sketch6 each of:
6
a) f x4 3
b) f x  4 2
2
-8
-6
-4
-2
2
x
2
4
6
8
-8
-6
-4
-2
x
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8
8. A team of biologists have discovered a new type of
rain forest. They note the temperature of the area
appears to vary over time in a cyclic, periodic
pattern. A maximum temperature of 90° occurs 3
hours after they start their examination. A
minimum temperature of 66° occurs 6 hours
later. The team would like to find a way to predict
the region’s temperature over time in hours. Your
task is to help them by creating a graph of two full
periods and an equation of temperature as a
function over time in hours.
9. Given each polynomial function, use an algebraic proof to determine if it is an even function, an odd function, or
neither.
a) f x   4 x 6  2 x 4  8
b) g x   4 x 5  6 x 3  7 x
10. Solve for x and check with your calculator:
56  x  x
11. Given the parabola  16 y  3  x  3 , identify:
a) the focus
b) the directrix
c) the nature of the roots
2
Questions 12 – 15 are multiple choice.
12. The equation 4 x 2  24 x  4 y 2  72 y  76 is equivalent to
(b) 4x  3  4 y  9  121
(a) 4x  3  4 y  9  76
2
2
2
(c) 4x  3  4 y  9  166
2
2
(d) 4x  3  4 y  9  436
2
2
2
13. Which value, to the nearest tenth, is not a solution of p(x) = (x) if px   x 3  3x 2  3x  1 and qx   3x  8 ?
(a) -3.9
(b) -1.1
(c) 2.1
(d) 4.7
a  5b  c  20
14. Which value is not contained in the solution of the system: 4a  5b  4c  19
 a  5b  5c  2
(a) -2
(b) 2
(c) 3
(d) -3
15. Given the graph of p(x) to the right, what is the remainder when
p(x) is divided by x + 4?
(a) x – 4
(b) -4
(c) 0
(d) 4