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35 Cards in this Set
- Front
- Back
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To shift a graph up, you must...
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Add on the outside of its function.
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To shift a graph down, you must...
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Subtract on the outside of the function.
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To shift a graph right, you must...
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Subtract on the inside of the function.
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To shift a graph left, you must...
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Add on the inside of the function.
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To reflect a graph over the x-axis, you must...
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Put the minus sign outside the function.
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To reflect a graph over the y-axis, you must...
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Put the minus sign inside the function.
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When a function is multiplied outside [y = c * f(x)], what happens to its graph?
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It shrinks/stretches vertically.
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When a function is multiplied inside [y = f(c * x)], what happens to its graph?
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It shrinks/stretches horizontally.
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If c > 1, how is y = c * f(x) transformed?
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It is stretched vertically by a factor of c.
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If 0 < c < 1, how is y = c * f(x) transformed?
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It is shrinked vertically by a factor of c.
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If c > 1, how is y = f(c * x) transformed?
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It is shrinked horizontally by a factor of 1/c.
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If 0 < x < 1, how is y = c * f(x) transformed?
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It is stretched horizontally by a factor of 1/c.
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When is a function even?
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1) When f(-x) = f(x) for all x in the domain of f.
2) Its graph is symmetric with respect to the y-axis. |
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When is a function odd?
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1) When f(-x) = -f(x) for all x in the domain of f.
2) Its graph is symmetric with respect to the origin. |
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A parabola opens upward when...
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when a > 0
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A parabola opens downward when...
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when a < 0
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What is the quadratic formula?
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f(x) = ax^2 + bx + c
(a, b, and c are real and a doesn't = 0 |
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What is the shape of any quadratic function?
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A parabola.
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What is the standard form of the quadratic formula?
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f(x) = a(x-h)^2 - k
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If a > 0, then what value of f is f(h) = k?
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The minimum value.
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If a < 0, then what value of f is f(h) = k?
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The maximum value.
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What is the local maximum value?
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The number f(a) when there is a rectangle such that the point (a, f(a)) is the largest point on the graph of f within the viewing rectangle (not on the edge).
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What is the local minimum value?
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The number f(b) when there is a rectangle such that the point (a, f(b)) is the lowest point on the graph of f within the viewing rectangle (not on the edge).
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What is the Completing the Square formula?
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(ax^2 + bx + c) = a(x + b/2a)^2 + c - b^2/4a
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What is the vertex formula?
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(-b/2a, c - b^2/4a)
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What does (f + g)(x) equal?
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f(x) + g(x)
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What does (f - g)(x) equal?
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f(x) - g(x)
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What does (fg)(x) equal?
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f(x)g(x)
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What does (f/g)(x) equal?
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(f(x))/(g(x))
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In f(g(x)), which function is applied first?
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g(x)
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One-to-one function
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A function in which no two elements of A have the same image
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Horizontal Line Test
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A function is one-to-one if and only if no horizontal line intersects its graph more than once
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Definition of the Inverse of a Function
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Let a one-to-one function have domain A and range B. Then its inverse function has domain B and range A.
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How to Find the Inverse of a One-to-One Function
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1) Write y = f(x).
2) Solve this equation for x in terms of y (if possible). 3) Interchange x and y. |
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Maximum/Minimum Value of a Quadratic Function
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x = - b / 2a
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