| Domain and Range | ||
| #1 | What is the domain of the following relation?
{(1,0), (3,4), (5,7), (7,8), (9,0)} |
{1, 3, 5, 7, 9) |
| #2 | What is the domain of the following relation?
{(0, .45), (.5, .75), (1, 1.26), (1.5, 2.3)} |
{0, .5, 1, 1.5} |
| #3 | What is the range of the following relation?
{(0,1), (3,5), (6,5), (10, 4), (12, 13)} |
{1, 5, 5, 4, 13} or {1, 5, 4, 13} |
| #4 | What is the range of the following relation?
{(2, 3), (4, 3), (6, 3), (8, 3)} |
{3, 3, 3, 3} or {3} |
| #5 | Look at the domain and range of the following relations. Determine which relation is also a function.
a. {(0, -1), (1, -1), (0, -2)}
b. {(-1, 1), (-1, -1), (0, 0)}
c. {(2, 1), (1, 0), (0, -1)}
d. {(-1, 1), (-1, 0), (-1, -1)} |
c. {(2, 1), (1, 0), (0, -1)} |
| Find the Range | ||
| #1 | Given the domain, find the range of this function.
f(x)= 3x(x+5)
Domain: {-2} |
f(-2)= 3(-2)(-2 + 5) f(-2)= (-6)(3)
f(-2)= -18 |
| #2 | For f(x)=3x2 - 5x, find f(-3). |
f(-3)= 3(-3)2 - 5(-3) f(-3)=3(9) +15 f(-3)= 27 +15
f(-3)= 42 |
| #3 | For f(x)= x3 - 6x, find f(4). |
f(4)= (4)3 - 6(4) f(4)= 64 - 24
f(4)=40 |
| #4 | Given the domain, {-5}, find the range of the following function.
f(x)= -|3 + x| |
f(-5)= -|3 + (-5)| f(-5)= -|-2| f(-5)= - (2)
f(-5)= -2 |
| #5 | Find the range of the following function for the domain {-2, -1, 0, 3}.
y=2 + x 4
|
{0, 1/4, 1/2, 5/4} or {0, .25, .5, 1.25} |
| Function Characteristics | ||
| #1 | Which function is a parabola, or has a U shape? |
Quadratic or x2 |
| #2 | Which function has a V shape? |
Absolute Value or |x| |
| #3 | A radical is always in what kind of function? |
Square Root |
| #4 | Which function is undefined at x=0 ? |
1/x or "no name" |
| #5 | Name a function that has only one vertex. |
Quadratic or Absolute Value |
| Translations and Reflections | ||
| #1 | Which axis has this function been reflected over?
f(x)= (-x)3 |
x-axis |
| #2 | Which axis is this function reflected over?
f(x)= -|x| |
y-axis |
| #3 | How has this function been translated?
f(x)= x2 + 6 |
Shifted up 6 units |
| #4 | How has this function been shifted?
f(x)= |x-3| |
Shift right 3 units |
| #5 | How has this function been shifted?
f(x)= (x+2)3 - 5 |
Shift left 2 units and down 5 units |
| Dilations | ||
| #1 | How has this function been stretched or shrunk?
f(x)= (6x)2 |
Horizontally Shrunk |
| #2 | How has this function been dilated?
f(x)= 1/2 |x| |
Veritcally Shrunk |
| #3 | How has this function been dilated?
f(x)= 4(x)3 |
Vertically Stretched |
| #4 | How has this function been dilated?
f(x)= (1/3x)3 |
Horizontally Stretched |
| #5 | In the equation y=6f(x), 6 would ______________ the graph. |
Verticalliy Stretch |
| Final Question | |
In what ways has this function been transformed?
f(x)= -3(x-2)2 + 7 |
Reflected over the y-axis Stretched Vertically by 3 Shifted right two units Shifted up 7 units |