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Transformations of absolute value functions: translations and reflections

AP Calculus AB AP Exam Review Free Response

3

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This Question is *

{ }^{*}

CALCULATOR INACTIVE**

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Please show all work on page

2 \& 3

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g

is defined and differentiable on the closed interval

[-6,6]

g(0)=4

y=g^{\prime}(x)

, the derivative of

g

, consists of a semicircle and three line segments, as shown in the figure below.

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x

-coordinate of each point of inflection of the graph

y=g(x)

on the interval

-6<x<6

. Explain your reasoning.

7

5

Initial Assessment - Maths ACSF

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Type your answer into the box.

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What is the value of

y

in the formula shown when

x=\frac{4}{5}

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y=\square \quad y=\frac{4}{x}+\sqrt{x+0.2}-5 x

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(Select the spanner to use a calculator.)

Ron was asked to determine whether

f(x)=\frac{1}{|x|}

is even, odd, or neither. Here is his work:

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1

: Find expression for

f(-x)

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\begin{aligned} f(-x) & =\frac{1}{|(-x)|} \\ & =\frac{1}{|x|} \end{aligned}

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2

f(-x)

f(x)

-f(x)

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\frac{1}{|x|}

f(x)=\frac{1}{|x|}

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3

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f(-x)

is equivalent to

f(x)

f

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Is Ron's work correct? If not, what is the first step where Ron made a mistake?

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1

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(A) Ron's work is correct.

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(B) Ron's work is incorrect. He first made a mistake in Step

1

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(C) Ron's work is incorrect. He first made a mistake in Step

2

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(D) Ron's work is incorrect. He first made a mistake in Step

3

A

B

each went on a quest to find food. Their displacements by the end are represented by vectors

\vec{a}

\vec{b}

, respectively.

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Which option best describes the meaning of the following statement?

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\| \vec{a} \| = \| \vec{b} \|

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1

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(A) The mice finished at the same distance from their starting points, but not necessarily in the same direction.

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(B) The mice finished at the same distance and in the same direction from their starting points.

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(C) The mice walked the exact same path.

CLEP College Mathematics

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16

60

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00

46

24

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A statistics exam consisted of three parts, Part

A

B

C

. The scores for Part

A

B

C

were, respectively, worth

20 \%, 30 \%

50 \%

of the total score of the exam. Nathan's score from Part

A

80 \%

of the score for Part

A

, his score from Part

B

B

2

of the score for Part

B

, and his overall score on the exam was

B

4

of the total score of the exam. What was Nathan's score from Part

C

in terms of a percent of the score for Part

C

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B

7

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Click on the answer box and type in a number. Backspace to erase.

\left\{\begin{array}{l} f(1)=-1.8 \\ f(n)=f(n-1) \cdot 9 \end{array}\right.

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Find an explicit formula for

f(n)

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f(n)=

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\square

Use the given information to prove that

\triangle H F G \cong \triangle E F D

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\overline{G D}

\overline{H E}

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\begin{array}{l} \overline{H E} \perp \overline{H G} \\ \overline{H E} \perp \overline{E D} \end{array}

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\triangle H F G \cong \triangle E F D \quad

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1

\square

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Given the vector

\mathbf{v}

has an initial point at

(8,8)

and a terminal point at

(8,6)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-1,4)

and a terminal point at

(1,6)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-2,0)

and a terminal point at

(-4,-3)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(0,6)

and a terminal point at

(2,0)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-1,3)

and a terminal point at

(-2,4)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(7,6)

and a terminal point at

(1,0)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-3,0)

and a terminal point at

(-5,-5)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-2,-6)

and a terminal point at

(-1,-4)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-7,4)

and a terminal point at

(-8,4)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-2,-3)

and a terminal point at

(-5,-2)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(7,2)

and a terminal point at

(2,6)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(0,2)

and a terminal point at

(-1,2)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(8,8)

and a terminal point at

(8,2)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-3,4)

and a terminal point at

(-6,4)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(0,-3)

and a terminal point at

(1,1)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(4,4)

and a terminal point at

(1,7)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(3,-4)

and a terminal point at

(6,-1)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-1,0)

and a terminal point at

(2,-3)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-1,-8)

and a terminal point at

(0,-5)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(5,1)

and a terminal point at

(4,-4)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-1,4)

and a terminal point at

(0,1)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(1,0)

and a terminal point at

(1,-6)

, find the exact value of

\|\mathbf{v}\|

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Given the vector

\mathbf{v}

has an initial point at

(-5,6)

and a terminal point at

(-6,1)

, find the exact value of

\|\mathbf{v}\|

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Lines, Functions, Systems

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Identifying solutions to a linear equation in two variables

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For each ordered pair, determine whether it is a solution to

x=-2

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\begin{tabular}{|c|c|c|}

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\hline \multirow{

2

(x, y)

} & \multicolumn{

2

}{|c|}{ Is it a solution? } \\

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2

3

} & Yes & No \\

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(3,0)

\bigcirc

\bigcirc

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(-8,5)

\bigcirc

\bigcirc

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(1,-2)

\bigcirc

\bigcirc

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(x, y)

1

\bigcirc

\bigcirc

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(x-4)(x-5)=0

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x=s

x=t

are the solutions to the given equation, which of the following is equal to the value of

|s-t|

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1

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-9

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-1

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1

(x-4)(x-5)=0

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x=s

x=t

are the solutions to the given equation, which of the following is equal to the value of

|s-t|

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1

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-9

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-1

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1

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9

Eva sees a dolphin

3

2

meters below sea level and a bird

\frac{47}{10}

meters above sea level.

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2

of the following expressions represents the vertical distance between the dolphin and the bird?

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2

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\left|\frac{47}{10}+3.2\right|

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\left|-3.2-\frac{47}{10}\right|

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\left|3.2-\frac{47}{10}\right|

We want to solve the following equation.

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|x-4|=x^{2}-6 x+9

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One of the solutions is

x \approx 1.4

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Find the other solution.

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Hint: Use a graphing calculator.

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Round your answer to the nearest tenth.

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x \approx

Fill in the blank.

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0.7_{--}|-6.7|

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1

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<

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>

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=

What is the modulus (absolute value) of

-6+4 i

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Don't round. If necessary, express your answer as a radical.

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|-6+4 i|=

What is the modulus (absolute value) of

-12+5 i

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Don't round. If necessary, express your answer as a radical.

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|-12+5 i|=

What is the modulus (absolute value) of

7-i

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Don't round. If necessary, express your answer as a radical.

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|7-i|=

What is the modulus (absolute value) of

15+8 i

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Don't round. If necessary, express your answer as a radical.

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|15+8 i|=

\mathrm{A}

\mathrm{B}

are moving along a plane. Their velocities are represented by vectors

\vec{a}

\vec{b}

, respectively.

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Which option best describes the meaning of the following statement?

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\|\vec{a}\|>\|\vec{b}\|

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1

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A

is heavier than particle

B

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(B) Particle A's speed is greater than particle B's speed.

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(C) Particle A's movement creates a greater counterclockwise angle with the eastward direction than particle B's movement.

\mathrm{A}

\mathrm{B}

are playing a game of tug of war. The forces in which they pull at the rope are represented by vectors

\vec{a}

\vec{b}

, respectively.

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Which option best describes the meaning of the following statement?

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\|\vec{a}\|=2|| \vec{b}||

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1

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(A) Team A has twice as many people as team

B

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(B) Team A pulls twice as strongly as team B.

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(C) Team A is twice as far from the center of the rope as team B.

A

B

each went on a quest to find food. Their displacements by the end are represented by vectors

\vec{a}

\vec{b}

, respectively.

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Which option best describes the meaning of the following statement?

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\|\vec{a}\|=\|\vec{b}\|

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1

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(A) The mice finished at the same distance from their starting points, but not necessarily in the same direction.

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(B) The mice finished at the same distance and in the same direction from their starting points.

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(C) The mice walked the exact same path.

What happens to the value of the expression

c+2

c

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1

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(A) It increases.

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(B) It decreases.

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(C) It stays the same.

What happens to the value of the expression

\frac{50}{p}

p

decreases from a large positive number to a small positive number?

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1

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(A) It increases.

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(B) It decreases.

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(C) It stays the same.

What happens to the value of the expression

b-1

b

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1

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(A) It increases.

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(B) It decreases.

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(C) It stays the same.

What happens to the value of the expression

\frac{q}{20}

q

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1

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(A) It increases.

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(B) It decreases.

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(C) It stays the same.

What happens to the value of the expression

\frac{10}{d}

d

increases from a small positive number to a large positive number?

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1

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(A) It increases.

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(B) It decreases.

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(C) It stays the same.

What happens to the value of the expression

\frac{5}{x}+5

x

decreases from a large positive number to a small positive number?

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1

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(A) It increases.

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(B) It decreases.

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(C) It stays the same.

The graph of a sinusoidal function intersects its midline at

(0,5)

and then has a maximum point at

(\pi, 6)

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Write the formula of the function, where

x

is entered in radians.

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f(x)=