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Stack #43102
| Question | Answer |
|---|---|
| what is a function represented by? | an equation, a graph, or a table |
| What is the domain of f(x) = x(square) - 2 | the set of all real numbers; its range is the set of all reals greater than or equal to -2 |
| Is f(-x) = -f(x) odd or even? | odd |
| Is f(-x) = f(x) odd or even? | even |
| Where is the graph of an odd function symmetric? | about the origin |
| Where is the graph of an even function symmetric about? | the y-axis |
| Is f(x) - .5x^3 odd or even? | odd; .5(-x)^3 = - f(x) |
| Is g(x) = 3x^2-1 odd or even? | even; g(-x) = 3(-x)^2-1 = 3x^-1 |
| What are the elements of the domain called? | inputs |
| What are the elements of the range called? | outputs |
| What does one-to-one mean? | any horizontal line cuts the graph of f in at most one point |
| What is the inverse of f? | f^-1 |
| What do you do to find the inverse of y= f(x)? | solve for x in terms of y, then interchange x and y |
| Find the inverse of f(x) = x^3-1 | solve the x: (3)(square root)y+1, then interchange x and y: y = (3)(square root)x+1 = f^-1(x) |
| Is f(x) = [x] the absolute-value function or the greatest-integer function? | the absolute-value function |
| Is g(x) = [x] the absolute-value function or the greatest integer function? | the greatest integer function |
| Describe what the absolute-value function (f(x)=[x] look like? | a V (origin at 0,0) |
| Describe what the greatest-integer function look like | ladders, and each "step" have an open circle at one end. The ladder is going in a positive direction |
| How would the graph of y = [f(x)] compare to y = f(x)? | The bottom of the graph would "fold up" to be with the top of the graph. The top of the graph stays where it is. |
| How would the graph of y = f([x]) compare with y = f(x) | the left side of the graph matches the right side. It's like everything on the left side of the graph "disappears" and becomes a mirror image of the right. |
| How does the graph y = -f(x) compares with y = f(x) | The graph "folds" along the x - axis. The top becomes the bottom and the bottom becomes the top. |
| How does the graph y = f(-x) compares with y = f(x) | The graph "folds" along the y - axis. The left side becomes the right side and the right side becomes the left. |
| What is a polynomial function | a(lower 0)x^n + a(lower 1)x^n-1 + a(lower 2)x^n-2; where n is positive or zero, and the a (coefficient) are constants |
| Linear function | f(x)= mx +b; where m = slope, b = y - intercepts |
| quadratic function | f(x) = ax^2 + bx + c; this is a parabola. When a>0 the grap opens up. When a<0 the graph opens down |
Created by:
Tiffastic