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38 Cards in this Set
- Front
- Back
Relation |
Pairs inputs with outputs |
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Function |
A relation that pairs each input with exactly one output. |
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Vertical Line Test |
A graph represents a function when no vertical line passes through more than one point on the graph. |
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Domain |
The set of all the possible input (x) values |
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Range |
The set of all the possible output (y) values |
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Independent Variable |
an input value, x-value |
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Dependent Variable |
an output value, y-value |
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Linear Function |
a function whose graph is a nonvertical line |
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Nonlinear Function |
a function that does not have a constant rate of change |
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Discrete domain |
a set of input values that consists of only certain numbers in an interval |
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Continuous domain |
a set of input values that consists of all numbers in an interval |
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Function Notation |
When f(x) (said "f of x") is used in place of y |
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Horizontal Lines are of the form |
y = b, where b is a constant |
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Vertical Lines are of the form |
x = b, where b is a constant |
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Standard Form of a Linear Equation is: |
Ax + By = C, x = C/A is the x-intercept and y= C/B is the y-intercept |
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x - intercept |
the x-coordinate of a point where the graph crosses the x-axis |
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y - intercept |
the y-coordinate of a point where the graph crosses the y-axis |
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Slope |
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Slope Intercept Form |
y = mx + b, m is the slope b is the y-intercept |
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Constant Function |
a linear function written in the form y=b since the slope would be 0. This is seen as a horizontal line. |
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Parent Function |
The most basic function in a family of functions. |
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Transformation |
Changes the size, shape, position, or orientation of a graph. |
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Translation |
A transformation that shifts the graph horizontally or vertically |
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Parent Function of a Linear Function |
f(x) = x |
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Horizontal Translation |
g(x) = f(x-h) When h is positive, (looks like subtraction) it is a horizontal translation to the right. When h is negative, (looks like addition) it is a horizontal translation to the left. |
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Horizontal Translation of f(x) = x 3 units to the left |
g(x) = f(x + 3) |
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Vertical Translation |
g(x) = f(x) + k When k is positive, it is a vertical translation up. When k is negative, it is a vertical translation down. |
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Vertical translation of f(x) = x, 7 units down |
g(x) = f(x) -7 |
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Reflection over the x-axis of f(x) = x |
g(x) = -f(x) |
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Reflection over the y-axis of f(x) = x |
g(x) = f(-x) |
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Vertical Shrink |
g(x) = af(x) when 0 < a < 1 |
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Vertical Stretch |
g(x) = af(x) when a > 1 |
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The graph of an absolute value function is always shaped like what letter? |
V |
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Vertex Form of an Absolute Value Function |
g(x) = a|x-h| + k The vertex would be (h,k) |
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What is the vertex of g(x) = 3|x+7|-4? |
(-7, -4) |
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Parent Function of an Absolute Value Function |
f(x) = |x| |
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f(x) = |x| ; g(x) = |x-1|+2 Describe the transformation from f to g |
The graph of g is a horizontal translation 1 unit right and a vertical translation 2 units up of the graph of f. |
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f(x) = x ; g(x) = 5f(x) Describe the transformation from f to g |
The graph of g is a vertical stretch by a factor of 5 of the graph of f. |