Math 3 Unit 1: Functions and Inverses
vertex form
The ____________ of a quadratic function is given by. f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.
decreasing
The graph of a function goes down on a portion of its domain when viewed from left to right.
range
The set of all possible output values of a function
standard form
The simplest way to show a number using digits.
maximum
The y-value of the highest point on the graph of a function
minimum
The y-value of the lowest point on the graph of a function
exponential function
f(x)=2^x domain: (-∞, ∞) range: [0, ∞)
step function
f(x)=[x]
standard form of any function
f(x)=a[b(x-h)]+k
cosine function
f(x)=cos(x) domain: (-∞, ∞) range: [-1, 1]
log rhythmic function (inverse exponential)
f(x)=log(x) domain: (0, ∞) range: (-∞, ∞)
sine function
f(x)=sin(x) domain: (-∞, ∞) range: [-1, 1]
linear function
f(x)=x domain: (-∞, +∞) range: (-∞, +∞)
quadratic function
f(x)=x^2 domain: (-∞, ∞) range: [0, ∞)
cubic function
f(x)=x^3 domain: (-∞, ∞) range: (-∞, ∞)
quartic function
f(x)=x^4 domain: (-∞, ∞) range: [0, ∞)
absolute value function
f(x)=|x| domain: (-∞, ∞) range: [0, ∞)
square root function
f(x)=√x domain: [0, ∞) range: [0, ∞)
increasing
from left to right, the graph goes up.
odd function
graph is symmetric with respect to the origin; f(-x)=-f(x)
even function
graph is symmetric with respect to the y-axis; f(-x)=f(x)
reflection over x-axis
negative (a) value
reflection over y-axis
negative (b) value
shift right
negative (h) value
shift down
negative (k) value
inverse of a function
opposite of the function (switch x and y)
shift left
positive (h) value
shift up
positive (k) value
end behavior
the behavior of the graph of a function as x approaches positive infinity or negative infinity
x-intercept
the x-coordinate of a point where a graph crosses the x-axis
y-intercept
the y-coordinate of a point where a graph crosses the y-axis
vertical compression
0<a<1 (wider)
horizontal stretch
0<b<1 (wider)
axis of symmetry
A line that divides a plane figure or a graph into two congruent reflected halves
relative maximum
A point on the graph of a function where no other nearby points have a greater y-coordinate.
relative minimum
A point on the graph of a function where no other nearby points have a lesser y-coordinate.
vertex
A point where two or more straight lines meet.
vertical stretch
a>1 (narrow)
domain
all the possible x-values of a function
horizontal compression
b>1 (narrow)
inverse function
f(x)= 1/x domain: (-∞, 0) U (0, ∞) range: (-∞, 0) U (0, ∞)