What is a dependant variable?
A variable whose value depends on that of another
In experiments, it is often the outcome that researchers measure.
What is an independent variable?
A variable that is manipulated to observe its effect on the dependant variable
It is the presumed cause in an experiment.
What does the equation y = F(x) represent?
A function where y is the output and x is the input
F(x) denotes the relationship between x and y.
What is the DOMAIN in a function?
The set of inputs for the function
It includes all possible x values.
What is the RANGE in a function?
The set of outputs for the function
It includes all possible y values.
What characterizes a monotonically increasing function?
f(a) < f(x) for x1 < x2
As x increases, f(x) does not decrease.
What characterizes a monotonically decreasing function?
f(x1) > f(x2) for x1 < x2
As x increases, f(x) does not increase.
What is a symmetric function about the y-axis?
An even function where f(x) = f(-x)
The graph is mirrored over the y-axis.
What is an odd function?
A function symmetric around the origin where f(-x) = -f(x)
The graph is reflected over the origin.
What are periodic functions?
Functions that repeat after a certain range of values, called the period T
Examples include sine and cosine functions.
What does ‘one-to-one’ mean in the context of functions?
Each input value gives only one output value
No two different inputs produce the same output.
What does ‘one-to-many’ mean?
One input value corresponds to more than one output value (NOT AN ACTUAL FUNCTION)
This situation does not qualify as a function.
What does ‘many-to-one’ mean?
Multiple input values give the same output value
This is a valid function type.
What are inverse functions?
Functions that reverse the operations of another function
If f(x) = y, then f^-1(y) = x.
How can linear functions be expressed?
As y = mx + b
m represents the slope and b the y-intercept.
What is the function f(x) when x ≥ 0?
f(x) = x
This defines the function for non-negative values of x.
What is the function f(x) when x < 0?
f(x) = -x
This defines the function for negative values of x.
How can quadratic functions be represented?
f(x) = ax² + bx + c
This is the standard form of a quadratic function.
What is the factored form of a quadratic function?
f(x) = a(x - d)² + e
This form indicates vertex form, where (d, e) is the vertex.
What characterizes a strictly proper rational function?
Degree of numerator is less than degree of denominator
This influences the behavior of the function as x approaches infinity.
What characterizes a proper rational function?
Degrees of numerator and denominator are the same
This means the leading coefficients dictate the end behavior.
What characterizes an improper rational function?
Degree of numerator is greater than degree of denominator
This can lead to asymptotic behavior.
What are rational functions?
Quotient (division) of two polynomials
They can be expressed as f(x) = P(x)/Q(x), where P and Q are polynomials.
