Free Printable 12. Module A Outcome 2 Piecewise and Absolute Value

1.

Check all of the boxes that are true statments.

a)

f(0) = 2

b)

f(-1) = 1

c)

The domain of the piecewise function is

$\left(-\infty,\infty\right)$

d)

f(-4) = -10

2.

Rewrite the absolute value function as a piecewise function

p\left(x\right)=\left|x+4\right|

a)

-x-4 x $\le$ -4
x+4 x $>$ -4

b)

-x-4 x $\ge$ -4

x+4 x $<$ -4

3.

Using the following absolute value f(x)=|x-4|-6 check all of the true statements.

a)

The vertex of the absolute value function is (4,-6)

b)

The Range of the absolute value function is
[−6,∞)

c)

The Domain of the absolute value function is (-inf,INF)

d)

An increasing interval of the absolute value is

(4, inf)

4.

Given the parent function f(x) =|x|, what transformations have taken place to get the new function f(x) = -2|x+4|+6. Check all that apply.

a)

The function has translations left four and up six

b)

The function has translations right four and up six

c)

The function is reflected over the x-axis

d)

The function has a vertical stretch of two

e)

The function has vertical compression of two

5.

Choose the Absolute Value function that is equivalent to the following Piecewise Function

a)

f(x) = 2|x+4|-1

b)

f(x) = 2|x-4|+1

c)

f(x) = -2|x+4| - 1

6.

Using the following absolute value f(x) =|x-4|-6 find where the graph is increasing and decreasing. Check all that apply

a)

The absolute value function is increasing from $\left(4,\infty\right)$

b)

The absolute value function is increasing from $\left[4,\infty\right)$

c)

The absolute value function is decreasing from $\left(-\infty,4\right)$

d)

The absolute value function is decreasing from $\left(-\infty,-4\right]$

7.

Given the parent function f(x ) =|x| , what transformations have taken place to get the new function f(x)= |2x|- 6. Check all that apply

a)

The absolute value has a vertical translation of down 6

b)

The absolute value has a horizontal compression of 1/2

c)

The absolute value has a horizontal stretch of 2

d)

The absolute value has a reflection about the x-axis.

8.

Use the graph of g(x) = 2|x|+1 determine all of the true statements.

a)

The vertex is a minimum at the point (0,1)

b)

The Vertex is a maximum at the point (0,1)

c)

The function is increasing from
$\left[0,\infty\right)$ , The function is decreasing on the interval $\left(-\infty,0\right]$

d)

The range of the function is $\left(-\infty,\infty\right)$

9.

Given the function h(x) = |2x-4| - 7 check all of the statements that are false.

a)

The vertex is ( 2, -7)

b)

The vertex is (4,-7)

c)

The x- intercepts of the absolute value function is x=-1.5 and x= 5.5

d)

[−7,∞)

The range of the function is [

10.

Convert the folowing absolute value functions to a piecewise function $g\left(x\right)\ =\ 2\left|x+3\right|-1$

a)

$2\left(-x-3\right)+1\ \ \ \ \ \ \ \ x<-3$ $2\left(x+3\right)\ +1\ \ \ \ \ \ \ \ \ \ x\ge-3$

b)

$-2x-7\ \ \ \ \ \ \ \ \ \ \ x<-3$ $2x+5\ \ \ \ \ \ \ \ \ \ \ \ x>-3$

c)

$-2x-7\ \ \ \ \ \ \ \ \ \ x\le-3$ $2x+5\ \ \ \ \ \ \ \ \ \ \ \ x>-3$

11.

Convert the following absolute value functions to a piecewise function $g\left(x\right)\ =\ 3\left|x-1\right|+2$ . Check all that apply.

a)

$-3\left(x-1\right)+2\ \ \ x<1$ $3\left(x-1\right)\ +2\ \ \ \ x\ge1$

b)

$-3x-5\ \ \ \ \ x<1$ $3x-1\ \ \ \ \ \ \ \ \ \ \ x>1$

c)

$-3x+5\ \ \ \ \ \ \ x\le1$ $3x-1\ \ \ \ x>1$

12. Module A Outcome 2 Piecewise and Absolute Value

Total questions: 11

Worksheet time: 7mins

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