Quiz about 12. Module A Outcome 2 Piecewise and Absolute Value

Question 1

Check all of the boxes that are true statments.

Accepted Answer

Accepted Answer

Accepted Answer

The domain of the piecewise function is

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

Answer

f(-4) = -10

Question 2

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.

Accepted Answer

The function has translations left four and up six

Accepted Answer

The function is reflected over the x-axis

Accepted Answer

The function has a vertical stretch of two

Answer

The function has translations right four and up six

Answer

The function has vertical compression of two

Question 3

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

Accepted Answer

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

Answer

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

Answer

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

Question 4

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

Accepted Answer

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

Accepted Answer

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

Answer

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

Answer

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

Question 5

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

Accepted Answer

The absolute value has a vertical translation of down 6

Accepted Answer

The absolute value has a horizontal compression of 1/2

Answer

The absolute value has a horizontal stretch of 2

Answer

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

Question 6

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

Accepted Answer

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

Answer

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

Answer

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

Question 7

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

Accepted Answer

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

Accepted Answer

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

Answer

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

12. Module A Outcome 2 Piecewise and Absolute Value