| Function Basics | ||
| #1 | What is the domain for the function?
3y f(x) = -------- y + 5 |
(-∞, -5) U (-5, ∞) or x ≠ -5 |
| #2 | What is the domain for the function?
y = √(3x+2) |
[-2/3, ∞) or x ≥ -2/3 |
| #3 | Determine if the equation is a function of x.
x2 +y2 = 4 |
No it is not a function of x. |
| #4 | Determine if the equation is a function of x.
|y|= 4x + 2 |
No it is not a function of x. |
| #5 | For what value(s) of x is f(x) = g(x)?
f(x) = x2 + 2x + 1 g(x) = 7x - 5 |
x = 2, 3 |
| Evaluating Functions | ||
| #1 | Evaluate f(x) = 3 - √x for f(9), f(0), and f(4x2). |
f(9) = 0 f(0) = 3 f(4x2) = 3 - 2x |
| #2 | Evaluate f(x) = |x| + 4 for f(-3) and f(2). |
f(-3) = 7 f(2) = 6 |
| #3 | Evaluate f(x) = [x - 2] + 5 for f(-2.5), f(-0.4) and f(1.24). |
f(-2.5) = 0 f(-0.4) = 2 f(1.24) = 4 |
| #4 | Evaluate the following function for f(-4), f(-1), and f(3).
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f(-4) = -1 f(-1) = 1 f(3) = -1 |
| #5 | Evaluate the following function for f(-2), f(1), and f(5).
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f(-2) = 4 f(1) = 2 f(5) = -1 |
| Analyzing a Graph | ||
| #1 | What are the intercepts of the graph of the function x2 + y = 4? |
(2,0) (-2,0) (0,4) |
| #2 | Identify all of the relative maximum(s) and minimum(s) of the graph:
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Maximums: (1,3), (6,8) Minimums: (-2,-1), (2,-4) |
| #3 | Determine the intervals on which the function is increasing, decreasing, or constant.
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Increasing: (-∞, -1), (0, 1) Decreasing: (-1, 0) Constant: (1, ∞) |
| #4 | Use the algebraic tests to test the graph for symmetry in the x-axis, the y-axis, and the origin.
x - y2 = 4 |
Symmetry in the x-axis. |
| #5 | Use the algebraic tests to test the graph for symmetry in the x-axis, the y-axis, and the origin.
y = x3 -2x |
Symmetry in the origin. |
| Families of Functions | ||
| #1 | What is the family of functions whose graph is a parabola, or a "U" shape? |
Quadratic Function |
| #2 | What is the family of functions for f(x) = |x|, whose graph is a "V" shape? |
Absolute Value Function |
| #3 | What is the family of functions with the following graph - |
Cubic Function |
| #4 | What is the parent function for the greatest integer function? |
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| #5 | What is the reciprocal function? |
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| Transformations | ||
| #1 | Describe the set of transformations from the parent function, f(x), to the graph of g(x).
g(x) = x2 - 3 |
Down 3. |
| #2 | Use function notation to write g(x) in terms of its parent function, f(x).
g(x) = -3[x + 3] - 4 |
g(x) = -3f(x + 3) - 4 |
| #3 | Write an equation for the function described by the given characteristics:
The shape of f(x) = x3, but shifed 12 units up and then reflected in the x-axis. |
g(x) = -(x3 + 12) or g(x) = -x3 - 12 |
| #4 | Describe the set of transformations from the parent function, f(x), to the graph of g(x).
g(x) = -|x - 2| + 4 |
Reflect in the x-axis, move right 2, and up 4. |
| #5 | Identify the parent function, f(x). Describe the set of transformations from the parent function, f(x), to the graph of g(x). Then use function notation to write g(x) in terms of its parent function, f(x).
g(x) = -√(-x + 2) - 4
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Square Root Function
Reflect in the x-axis, and the y-axis. Move left 2 and down 4.
g(x) = -f(-x + 2) - 4 |
| Final Question | |
What is Mrs. Poole's favorite college team? |
Iowa State Cyclones!!!
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