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Precalculus Unit 1
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Terms in this set (41)
implied domain
the domain of a function's algebraic expression
relevant domain
the domain that fits the situation of the model
local maximum
a turning point that is higher than all nearby points on a graph
absolute maximum
highest point on a graph
local minimum
a turning point that is lower than all nearby points on a graph
absolute minimum
the lowest point on a graph
odd function
f(-x)=-f(x) - symmetrical
even function
f(-x)=f(x) - asymmetrical
open circle represents...
a value that is not included in the set
closed circle represents...
a value that is included in the set
vertical shift c units upwards
h(x) = f(x)+c
vertical shift c units downwards
h(x) = f(x)-c
horizontal shift c units to the right
h(x) = f(x-c)
horizontal shift c units to the left
h(x) = f(x+c)
reflection in the x axis
h(x) = -f(x)
reflection in the y axis
h(x) = f(-x)
rigid transformation
horizontal shifts, vertical shifts, and reflections
nonrigid transformation
distorts function, looks different
vertical shrink
if g(x)=cf(x) and c is a fraction or decimal - example: 0.25f(x)
vertical stretch
if g(x)=cf(x) and c is greater than 1 - example: 4f(x)
horizontal stretch
if g(x)=f(cx) and c is a fraction or decimal - example: f(0.25x)
horizontal shrink
if g(x)=f(cx) and c is greater than 1 - example: f(4x)
parent functions from this unit
f(x) = x (identity function)
f(x) = x^2 (squaring function)
f(x) = x^3 (cubing function)
f(x) = 1/x (reciprocal function)
f(x) = square root of x (square root function)
f(x) = e^x (exponential function)
f(x) = absolute value of x (absolute value function)
f(x) = greatest integer function
adding functions
(f+g)(x) = f(x) + g(x)
subtracting functions
(f-g)(x) = f(x) - g(x)
dividing functions
(f/g)(x) = f(x) divided by g(x)
multiplying functions
(fg)(x) = f(x) * g(x)
composition of functions
(fog)(x)=f(g(x))
inverse functions
two functions f and g are inverse functions if both of their compositions equal x
functions must be ____ to have an inverse
one-to-one
how can you tell if a graph is one-to-one?
horizontal line test
positive correlation
points on a graph seem to increase linearly
negative correlation
points on a graph seem to decrease linearly
no correlation
no apparent increase or decrease of points on a graph; or a combination of the two
correlation numbers
the closer to 1 or -1 the correlation number is, the more accurate the best fit line is to the data.
f(x)=x
f(x)=x^2
f(x)=x^3
f(x)=1/x
f(x)=square root of x
f(x)=|x|
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