Free Printable Characteristics of Piecewise Function

1.

What is the y intercept?

a)

(0, 5.5)

b)

(5.5, 0)

c)

(-2.1, 0)

d)

(0, -2.1)

2.

What is the x intercept?

a)

(0, 5.5)

b)

(5.5, 0)

c)

(-2, 0)

d)

(0, -2)

3.

What is the DOMAIN?

Hint: Domain is the set of x-values. Be careful when there are restrictions/exemptions of the x-values. This happens when there are gaps (meaning jumps, holes or asymptotes) in the graph.

a)

(-∞, +∞)

b)

(-∞, -1] U [3, +∞)

c)

[-1, +∞)

d)

(-1, 0] U (0, +∞)

4.

Graph the piecewise function. You may use desmos graphing calculator. Type $g\left(x\right)=3x-1\left\{x\ge-1\right\}$ and $g\left(x\right)=-5\ \left\{x<-1\right\}$ . Whenever you graph the function and there are restrictions in the domain, you have to type { }, This is true to all restrictions. Be careful to determine the portions of the graph that have shaded (inclusive) and unshaded (exclusive) points because desmos does not show directly these type of points. For > and < it should be unshaded points while $\ge and\ \le$ should be shaded points.

a)

b)

c)

d)

5.

Select the correct domain for this piecewise function.

a)

$\left[-3,\ 1\right]$

b)

$\left[-12,\ 8\right]$

c)

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

d)

$\left[-6,\ 4\right]$

6.

Select the correct range for this piecewise function.

a)

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

b)

$\left[-12,\ 8\right]$

c)

$\left[-6,\ 4\right]$

d)

$\left[-3,\ 1\right]$

7.

Which of the following represents this peicewise graph.

Hint: Try to match the functions with the graph. You should know how to graph piecewise functions. You may go back to the slides posted in Google classroom or refer to your notes.

a)

b)

c)

d)

8.

What is the domain of the above piecewise function?

Hint: Domain is the set of x-values. Be careful when there are restrictions/exemptions of the x-values. This happens when there are gaps (meaning jumps, holes or asymptotes) in the graph.

a)

$D:\ x=all\ real\ numbers$

b)

$D:\ x\ge2$

c)

$D:\ x\le-1\ or\ x\ge1$

d)

$D:\ y>2$

e)

none of these are correct.

9.

Which of the following piecewise functions represents the graph above?

a)

b)

c)

d)

e)

none of these are correct.

10.

State the range of the above piecewise function.

Hint: Range is the set of y-values. Be careful when there are restrictions/exemptions of the y-values.

a)

R: y = All real Numbers

b)

$R:\ y<4\ or\ y\ge1$

c)

$R:\ y<4\ or\ y\ge1$

d)

$R:\ y<4$

e)

none of these are correct.

11.

Which of the following represents the above piecwise function?

a)

b)

c)

d)

12.

State the range of the following Piecewise Function:

Hint: Range is the set of y-values. Be careful when there are restrictions/exemptions of the y-values.

a)

$R:\ y\le2\$

b)

R: y = All real numbers

c)

$R:\ y<0$

d)

$R:\ y=2\ or\ \ y<0\$

e)

None of these are correct.

13.

State the domain of the above piecewise function.

Hint: Domain is the set of x-values. Be careful when there are restrictions/exemptions of the x-values. This happens when there are gaps (meaning jumps, holes or asymptotes) in the graph.

a)

D: x = All real numbers

b)

$D:\ y<4$ or $y\ge1$

c)

$D:\ x<2\ or\ x>2$

d)

$D:\ y<4$

e)

none of these are correct.

14.

Which piecewise function corresponds to this graph? (Take your time). Hint: Try to match the function with the graph. You should know how to graph piecewise functions. You may go back to the slides posted in Google classroom or refer to your notes.

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

15.

The graph represents a piecewise function. How many pieces make up the function?

a)

1

b)

2

c)

3

d)

4

16.

State the location of any discontinuities (Select all that apply). Hint: discontinuities refer to the restrictions or exemptions of the x-value/s. Discontinuities happen if there are gaps (meaning jumps, holes or asymptotes) in the graph. There are two answers for this number.

a)

At x = 2

b)

At x = 1

c)

This graph has no discontinuities

d)

At x = 3

17.

This piecewise function is a combination of at least how many functions?

a)

0

b)

1

c)

2

d)

3

18.

What is the equation of the RED piece (one on the RIGHT)?

a)

x - 1 if x > 3

b)

3 if x ≥ 3

c)

-1 if x ≥ 3

d)

-1 if x > 3

19.

Select the correct range for this piecewise function.

a)

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

b)

$\left[-12,\ 8\right]$

c)

$\left[-6,\ 4\right]$

d)

$\left[-3,\ 1\right]$

20.

On what intervals of x is f(x) decreasing? (select all answers)

a)

$-9\le x\le-3$

b)

$3\le x\le9$

c)

$x\le-6$

d)

$0\le x\le6$

21.

During which interval is the bicyclist moving the fastest?

a)

$0\le t\le2$

b)

$2\le t\le4$

c)

$4\le t\le7$

d)

$1\le t\le3$

22.

Select ALL the statements that are true. Hint: Piecewise Function is kind of different from the regular function in terms of how the intervals are written. For the piecewise function intervals, use [ ] for shaded circles and ( ) for unshaded circles.

a)

The constant interval is [-4, 2]

b)

The interval of increase is [-6, -4]

c)

The interval of decrease is (-9, -6] U (2, ∞)

d)

There is a discontinuity at x = 2

e)

The range is (-∞, 8)

23.

Select ALL the statements that are true. Hint: This may have one or more than one correct answer. Be careful of the exemptions of the values. This happens when there's a gap (either a jump, hole or an asymptote)

a)

There are 2 y-intercepts

b)

The domain is [-10, 10]

c)

The range is [-7, 4)

24.

Which statement is FALSE?

a)

-4 is included in the domain, but 4 is not

b)

The interval of decrease is [-4, 0]

c)

The interval of increase is [-1, 2]

d)

The interval of increase is [0, 2]

25.

Functions that are made up of distinct "pieces" of other functions defined over different intervals are called

a)

Absolute Value Functions

b)

Piecewise Functions

c)

Exponential Functions

d)

Quadratic Functions

Characteristics of Piecewise Function

Total questions: 25

Worksheet time: 3hrs 51mins

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