NYS

These are the resources that support this NYS Standard.

NY-AI-F.IF.7: Graph functions and show key features of the graph by hand and by using technology where appropriate.

There are 866 resources.
Title Description Thumbnail Image Curriculum Topics

Definition--Calculus Topics--Inflection Point

Definition--Calculus Topics--Inflection Point

The point on a curve where the curvature changes. This is often indicated by a change in the slopes of tangents to the curve.

Definition--Calculus Topics--Inflection Point Calculus Vocabulary

Definition--Calculus Topics--Instantaneous Rate of Change

Definition--Calculus Topics--Instantaneous Rate of Change

Another way of describing the slope of the line tangent to a given curve at a given point.

Definition--Calculus Topics--Instantaneous Rate of Change Calculus Vocabulary

Definition--Calculus Topics--Integral

Definition--Calculus Topics--Integral

A method for finding the area of a curve along an interval. In calculus, integrating a function f(x) involves finding the antiderivative of f(x).

Definition--Calculus Topics--Integral Calculus Vocabulary

Definition--Calculus Topics--Integral Symbol

Definition--Calculus Topics--Integral Symbol

The mathematical symbol used to denote the process of integration. The symbol is an elongated S, which indcates the infinitesimal sums that make up the area under a curve.

Definition--Calculus Topics--Integral Symbol Calculus Vocabulary

Definition--Calculus Topics--Integrand

Definition--Calculus Topics--Integrand

In the process of integration, it is the function that is being integrated.

Definition--Calculus Topics--Integrand Calculus Vocabulary

Definition--Calculus Topics--Integration by Substitution

Definition--Calculus Topics--Integration by Substitution

Replacing the integrand with a simpler expression to make the process of integration easier.

Definition--Calculus Topics--Integration by Substitution Calculus Vocabulary

Definition--Calculus Topics--Intermediate Value Theorem

Definition--Calculus Topics--Intermediate Value Theorem

For continuous function f(x) along interval [a, b] there are values between f(a) and f(b).

Definition--Calculus Topics--Intermediate Value Theorem Calculus Vocabulary

Definition--Calculus Topics--Inverse Function

Definition--Calculus Topics--Inverse Function

For function f(x), the inverse function f-1(x), if it exists, undoes the mapping of the original function.

Definition--Calculus Topics--Inverse Function Calculus Vocabulary

Definition--Calculus Topics--L'Hopital's Rule

Definition--Calculus Topics--L'Hopital's Rule

For function f(x)/g(x), where f(x) and g(x) are two functions, along an interval [a, b], if there is a point c in the interval such that g(x) = 0, then L'Hopital's Rule can be used to find the limit as x approaches c by taking the ratio of the derivatives of the two functions.

Definition--Calculus Topics--L'Hopital's Rule Calculus Vocabulary

Definition--Calculus Topics--Left-Hand Limit

Definition--Calculus Topics--Left-Hand Limit

As a function f(x) approaches a specific input value a, for x-values less than or equal to a, the function may approach a specific limiting value. This limit may or may not exist.

Definition--Calculus Topics--Left-Hand Limit Calculus Vocabulary

Definition--Calculus Topics--Limit

Definition--Calculus Topics--Limit

As a function f(x) approaches a specific input value a, the function may approach a specific limiting value. This limit may or may not exist.

Definition--Calculus Topics--Limit Calculus Vocabulary

Definition--Calculus Topics--Limits at Infinity

Definition--Calculus Topics--Limits at Infinity

Finding the limiting value for function f(x) as the input value x approaches infinity. This limit may or may not exist.

Definition--Calculus Topics--Limits at Infinity Calculus Vocabulary

Definition--Calculus Topics--Linear Approximation

Definition--Calculus Topics--Linear Approximation

For differentiable function f(x), the linear approximation at x = a, for some real number a, is the equation of the line tangent to f(x) at a.

Definition--Calculus Topics--Linear Approximation Calculus Vocabulary

Definition--Calculus Topics--Local Maximum

Definition--Calculus Topics--Local Maximum

When a function takes an input value, a, for some region in the domain, such that f(a) ≥ f(x), for all x in that region. A function can have more than one local maximum.

Definition--Calculus Topics--Local Maximum Calculus Vocabulary

Definition--Calculus Topics--Local Minimum

Definition--Calculus Topics--Local Minimum

When a function takes an input value, a, for some region in the domain, such that f(a) ≤ f(x), for all x in that region. A function can have more than one local minimum.

Definition--Calculus Topics--Local Minimum Calculus Vocabulary

Definition--Calculus Topics--Matrix Representations of Vectors

Definition--Calculus Topics--Matrix Representations of Vectors

A vector quantity can be represented by a matrix.

Definition--Calculus Topics--Matrix Representations of Vectors Calculus Vocabulary

Definition--Calculus Topics--Mean Value Theorem

Definition--Calculus Topics--Mean Value Theorem

For differentiable function f(x) along the closed interval [a, b] there is a value c within that interval such that f'(c) is parallel to the secant formed by the line connecting the endpoints of the interval.

Definition--Calculus Topics--Mean Value Theorem Calculus Vocabulary

Definition--Calculus Topics--Oblique Asymptote

Definition--Calculus Topics--Oblique Asymptote

A slanted line that the graph of a function approaches but does not intersect. The equation of an oblique asymptote is y = mx + b, for some constants m and b.

Definition--Calculus Topics--Oblique Asymptote Calculus Vocabulary

Definition--Calculus Topics--Odd Function

Definition--Calculus Topics--Odd Function

A function whose graph has point symmetry about the origin.

Definition--Calculus Topics--Odd Function Calculus Vocabulary

Definition--Calculus Topics--One-Sided Limits

Definition--Calculus Topics--One-Sided Limits

Restricting the limit of a function for values approaching the limiting value from one side.

Definition--Calculus Topics--One-Sided Limits Calculus Vocabulary

Definition--Calculus Topics--Parametric Equations

Definition--Calculus Topics--Parametric Equations

A set of equations where each variable, x and y, is a function of a third variable, t. Graphs of parametric equations are sometimes not functions.

Definition--Calculus Topics--Parametric Equations Calculus Vocabulary

Definition--Calculus Topics--Piecewise Function

Definition--Calculus Topics--Piecewise Function

A function made up of separate functions, each with its own interval.

Definition--Calculus Topics--Piecewise Function Calculus Vocabulary

Definition--Calculus Topics--Power Function

Definition--Calculus Topics--Power Function

A function with a single term that consists of a variable base raised to a real number power. The variable can also have a real number coefficient.

Definition--Calculus Topics--Power Function Calculus Vocabulary

Definition--Calculus Topics--Power Rule

Definition--Calculus Topics--Power Rule

The process of finding the derivative of a power function.

Definition--Calculus Topics--Power Rule Calculus Vocabulary

Definition--Calculus Topics--Quotient Rule

Definition--Calculus Topics--Quotient Rule

The rule for finding the derivative of a function made up of the ratios of two functions f(x) and g(x).

Definition--Calculus Topics--Quotient Rule Calculus Vocabulary