DOUGHERTY GRADUATION TEST PREP 2-22-11 ANSWERS

Diagnostic Answer Key

1.       D (does "general” form mean vertex form? Do students need to know this terminology?)

2.       B

3.       A

4.       D (confusing wording)

5.       D

6.       A

7.       C (can rate of change be at ONE point? If so, then A and C are both correct, right?)

8.       B

9.       D

10.   E

11.   C

12.   B

13.   C

14.   B

15.   B (computer says C)

16.   D (computer says B)

17.   A

18.   D

19.   D

20.   C

Dougherty High Graduation test Prep 2-22-11 1

 

GHSGT Math Express Diagnostic Pretest

Top of Form

1.

1. Change Y = X²-4x-11 into general form

a.   (x-2)²-11

b.   (x-2)²_+-4

c.   (x+2)²-15

d.   (x-2)²-15 

  2.The vertex of a parabola is (-2,7).  Which describes the horizontal and

     vertical transformations performed on the basic function to produce this

     parabola?

	a. Shift right 2 units and shift down 7 units
	b. Shift left 2 units and shift up 7 units
	c. Shift left 7 units and shift up 2 units
	d. Shift right 7 units and shift down 2 units

3.  A steady rate of change is represented by what type of function

	a. Linear
	b. Parabola
	c. Quadratic
	d. constant

4.   A line and a parabola can

	a. Intersect in one place
	b. Can never intersect
	c. Can intersect in only one place
	d. all of the above

5. If k (-2) = 0.5 Then find k^-1(0.5)

a.   k^-1(0.5) = 5

b.   k^-1(0.5) = -0.5

c.   k^-1(0.5) = 2

d.    k^-1(0.5) = -2

6.   The number 0 in a coefficient matrix means that

	a. the variable does not exist
	b. the variable is negative
	c. the variable has a coefficient of 1
	d. there is no solution to the equation

8(14). Evaluate  -a-a^1/3. When a = 8

A.     0

B.    -10

C.     -6

D.    -8

9(15). When an equation represents the function y = 6^x after it has been flipped over the y-axis and moved to the right 3 units?

a. y = 6^-x+3     b. y = 6^-x-3    c. y = -6^x+3     d. y = -6^x-3  

10(16).   Which statement is true about the end behavior of the graph of

        f(x) = - 5(0.2)^x

	a. As x approaches infinity, f(x) approches infinity. As x approches negative infinity, f(x) approaches 0.
	b. As x approaches infinity, f(x) approaches 0. As x approaches negative infinity, f(x) approaches infinity.
	c. As x approaches infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches 0.
	d. As x approaches infinity, f(x) approaches 0. As x approaches negative infinity, f(x) approaches negative infinity.

      

 

7(12)   The owl population in a national park can be modeled b the equation

        y = 4.85(1.07)^x, where x represents the number of years since 1970 and

        y represents the number of owls.  Use the equation to predict the owl            

        population in the year 2015

	a. 52
	b. 102
	c. 200
	d. 234

Dougherty High Graduation Test Preparation-6 Absolute Value

 Math Worksheets

|12| = _______________

|-7| = _______________

|17| = _______________

|29| = _______________

|-31| = _______________

|-26| = _______________

|-39| = _______________

|43| = _______________

|-30| = _______________

|-28| = _______________

Find the Absolute Value

Student Name: __________________________

|12| =

 Math Worksheets Answers12

|-7| =

7

|17| =

17

|29| =

29

|-31| =

31

|-26| =

26

|-39| =

39

|43| =

43

|-30| =

30

|-28| =

28

Student Name: __________________________ Score:

Dougherty High Graduation Test Preparation-5 Absolute Value

http://www.quia.com/cb/117518.html

Dougherty High Graduation Test Preparation-4 Absolute Value

1.

Function Families Worksheet #2

Algebra 2: Absolute Value

Graph each “family” of equations on a graphing calculator. Try to discover what

makes each one different. Then try to sketch them on the coordinate plane. Use

different colors to differentiate between the equations. Be sure to compare the

parts of the equation to the graph. Then, in your notebook, write what you have

discovered about the equations.

1. f(x) = | x | 2. f(x) = | x + 2 |

f (x) = | x | + 1 f(x) = | x - 2 |

f(x) = | x | - 4 f(x) = | x + 5 |

f(x) = | x | + 3 f(x) = | x - 3 |

3. f(x) = | 0.5x | 4. f(x) = | x + 4|

f(x) = |2 x | f(x) = | x | + 4

f(x) = | 3x| f(x) = - | x + 4 |

f(x) = | 6x | f(x) = - |x| + 4

pg. 1

5. f(x) = - | x | + 1 6. f(x) = | x + 1 | + 2

f(x) = - | x + 1 | f(x) = | x + 1 | - 2

f(x) = - | x - 3 | f(x) = | x - 1 | + 2

f(x) = - | x | - 3 f(x) = | x - 1 | - 2

For each equation below, identify the coordinates of the vertex of the graph.

Do this without actually graphing.

1. f(x) = | 6x | 2. f(x) = - | 2x|

vertex:____________ vertex:____________

3. f(x) = | x + 7 | 4. f (x) = | x | - 9

vertex:____________ vertex:____________

5. f(x) = | x + 8 | 6. f(x) = | x - 6 | + 8

vertex:____________ vertex:____________

7. f(x) = | x + 10 | + 12 8. f(x) = | x + 7 | - 8

vertex:____________ vertex:____________

pg. 2

Dougherty High Graduation Test Preparation-3 domain, range

1

Domain and Range of piecewise function

http://www.analyzemath.com/Graphing/piecewise_functions.html

 http://mathdemos.gcsu.edu/mathdemos/domainrange/domainrange.html

Vertex of piecewise function

http://www.brightstorm.com/math/precalculus/introduction-to-functions/domain-restrictions-and-functions-defined-piecewise

2, 

 

Dougherty High Graduation Test Preparation-2

1.

Inequalities and Absolute Value

Concepts "Piecewise Functions"

and Absolute Value

Kenny M. Felder

This work is produced by The Connexions Project and licensed under the

Creative Commons Attribution License

y

Abstract

This module introduces piecewise functions for the purpose of understanding absolute value equations.

What do you get if you put a positive number into an absolute value? Answer: you get that same number

back. /

positive

OK, so, what happens if you put a

number back, but made positive. OK, how do you

5/ = 5. j j= . And so on. We can say, as a generalization, that j x j= x; but only if x is.negative number into an absolute value? Answer: you get that samemake a negative number positive? Mathematically, you

multiply it by 1

. j 􀀀5 j= 􀀀(􀀀5) = 5. j 􀀀 j= 􀀀(􀀀 ) = . We can say, as a generalization, that

j

So the absolute value function can be de ned like this.

x j= 􀀀x; but only ifx is negative.

The Piecewise De nition of Absolute Value

j

x j= f

x; x

0

􀀀

x; x < 0

(1)

If you've never seen this before, it looks extremely odd. If you try to pin that feeling down, I think you'll

nd this looks odd for some combination of these three reasons.

1. The whole idea of a piecewise function that is, a function which is de ned di erently on di erent

domains may be unfamiliar. Think about it in terms of the function game. Imagine getting a card

that says If you are given a positive number or 0, respond with the same number you were given. If

you are given a negative number, multiply it by 1 and give that back. This is one of those can a

function

are more common than you might think.

2. The

But if

think of it as change the sign of

3. Even if you get past those objections, you may feel that we have taken a perfectly ordinary, easy to

understand function, and rede ned it in a terribly complicated way. Why bother?

do that? moments. Yes, it can and, in fact, functions de ned in this piecewise manner 􀀀x looks suspicious. I thought an absolute value could never be negative! Well, that's right.x is negative, then 􀀀x is positive. Instead of thinking of the 􀀀x as negative x it may help tox.

Version 1.4: Mar 24, 2010 1:21 pm GMT-5

y

http://creativecommons.org/licenses/by/2.0/

http://cnx.org/content/m18200/1.4/

Connexions module: m18200 2

Surprisingly, the piecewise de nition makes many problems

You already know how to graph

de nition. On the right side of the graph (where

graph (where

easier. Let's consider a few graphing problems.y =j x j. But you can explain the V shape very easily with the piecewisex 0), it is the graph of y = x. On the left side of thex < 0), it is the graph of y = 􀀀x.

(a) (b)

(c)

Figure 1:

where

where

(a) y = 􀀀 x The whole graph is shown, but the only part we care about is on the left,x < 0 (b) y = x The whole graph is shown, but the only part we care about is on the right,x 0 (c) y = j x j Created by putting together the relevant parts of the other two graphs.

Still, that's just a new way of graphing something that we already knew how to graph, right? But now

consider this problem: graph

becomes a snap.

y = x+ j x j. How do we approach that? With the piecewise de nition, it

x

+ j x j = f

x

+ x = 2x x 0

x

+ ( 􀀀 x ) = 0 x < 0

(2)

So we graph

drawings, as I did above.)

y = 2x on the right, and y = 0 on the left. (You may want to try doing this in three separate

http://cnx.org/content/m18200/1.4/

Connexions module: m18200 3

Figure 2:

y = x + j x j

Our nal example requires us to use the piecewise de nition of the absolute value for both

x and y.

Example 1: Graph |x|+|y|=4

We saw that in order to graph

j x j we had to view the left and right sides separately. Similarly,

j

y j divides the graph vertically.

On top, where y 0, j y j= y.

Since this equation has

horizontally and vertically, which means we look at

4

Where y < 0, on the bottom, j y j= 􀀀y.both variables under absolute values, we have to divide the graph botheach quadrant separately. j x j + j y j=

Second Quadrant First Quadrant

x

y

0, so j x j= 􀀀x x 0, so j x j= x 0, so j y j= y y 0, so j y j= y

(

􀀀x) + y = 4 x + y = 4

y

= x + 4 y = 􀀀x + 4

Third Quadrant Fourth Quadrant

x

y

0, so j x j= 􀀀x x 0, so j x j= x 0, so j y j= 􀀀y y 0, so j y j= 􀀀y

(

􀀀x) + (􀀀y) = 4 x + (􀀀y) = 4

y

= 􀀀x 􀀀 4 y = x 􀀀 4

Table 1

Now we graph each line, but only in its respective quadrant. For instance, in the fourth quadrant,

we are graphing the line

fourth quadrant.

y = x 􀀀 4. So we draw the line, but use only the part of it that is in the

http://cnx.org/content/m18200/1.4/

Connexions module: m18200 4

Figure 3

Repeating this process in all four quadrants, we arrive at the proper graph.

Figure 4:

j x j + j y j= 4

http://cnx.org/content/m18200/1.4/

Connexions module: m18200 1