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--Derivative of a Logarithmic Function

Definition--Calculus Topics--Derivative of a Logarithmic Function

The derivative of a logarithmic function uses the laws of logarithms and the definition of e to find the derivative.

Definition--Calculus Topics--Derivative of a Logarithmic Function Calculus Vocabulary

Definition--Calculus Topics--Derivative of a Polynomial Function

Definition--Calculus Topics--Derivative of a Polynomial Function

The derivative of a polynomial of degree n is another polynomial of degree n - 1.

Definition--Calculus Topics--Derivative of a Polynomial Function Calculus Vocabulary

Definition--Calculus Topics--Derivative of a Quadratic Function

Definition--Calculus Topics--Derivative of a Quadratic Function

Since a quadratic function is a polynomial function of degree 2, the derivative is a linear function.

Definition--Calculus Topics--Derivative of a Quadratic Function Calculus Vocabulary

Definition--Calculus Topics--Derivative of a Rational Function

Definition--Calculus Topics--Derivative of a Rational Function

Since a rational function is the ratio of two polynomials, the derivative of a rational function is also the ratio of two polynomials. This means the derivative of a rational is also rational.

Definition--Calculus Topics--Derivative of a Rational Function Calculus Vocabulary

Definition--Calculus Topics--Derivative of a Trig Function

Definition--Calculus Topics--Derivative of a Trig Function

The derivative of a trig function is another trig function, as shown in the table.

Definition--Calculus Topics--Derivative of a Trig Function Calculus Vocabulary

Definition--Calculus Topics--Derivative of an Exponential Function

Definition--Calculus Topics--Derivative of an Exponential Function

The derivative of an exponential function is the product of the function and the natural log of the base. The derivative of ex is ex.

Definition--Calculus Topics--Derivative of an Exponential Function Calculus Vocabulary

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function

Use implicit differentiation and the quotient rule to find the derivative of an inverse trig function.

Definition--Calculus Topics--Derivative of the Inverse of a Trig Function Calculus Vocabulary

Definition--Calculus Topics--Differentiable Function

Definition--Calculus Topics--Differentiable Function

A function is differentiable if a derivative can be found at each point in its domain.

Definition--Calculus Topics--Differentiable Function Calculus Vocabulary

Definition--Calculus Topics--Differential Equation

Definition--Calculus Topics--Differential Equation

An equation that includes the derivative of a function f(x) and the variable x.

Definition--Calculus Topics--Differential Equation Calculus Vocabulary

Definition--Calculus Topics--Differentiation

Definition--Calculus Topics--Differentiation

The process of finding the derivative of a function.

Definition--Calculus Topics--Differentiation Calculus Vocabulary

Definition--Calculus Topics--Discontinuous Function

Definition--Calculus Topics--Discontinuous Function

A function is discontinuous if it has one or more gaps along the domain of the function. The left- or right-hand limits exist but are not equal.

Definition--Calculus Topics--Discontinuous Function Calculus Vocabulary

Definition--Calculus Topics--Discrete Function

Definition--Calculus Topics--Discrete Function

A function whose graphs has gaps. This is because the function consists of separate ordered pairs or is a discontinuous function with gaps.

Definition--Calculus Topics--Discrete Function Calculus Vocabulary

Definition--Calculus Topics--Displacement Function

Definition--Calculus Topics--Displacement Function

A distance-vs.-time function used to find the distance an object has moved from a starting point. The function takes into account initial speed and acceleration.

Definition--Calculus Topics--Displacement Function Calculus Vocabulary

Definition--Calculus Topics--End Behavior

Definition--Calculus Topics--End Behavior

The way a function f(x) changes as x approaches infinity, whether positive or negative.

Definition--Calculus Topics--End Behavior Calculus Vocabulary

Definition--Calculus Topics--Even Function

Definition--Calculus Topics--Even Function

A function whose graph is symmetric about the y-axis.

Definition--Calculus Topics--Even Function Calculus Vocabulary

Definition--Calculus Topics--Explicit Function

Definition--Calculus Topics--Explicit Function

A function in which y can be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equation.

Definition--Calculus Topics--Explicit Function Calculus Vocabulary

Definition--Calculus Topics--Extreme Value Theorem

Definition--Calculus Topics--Extreme Value Theorem

For function f(x) along an interval, there are maximum and minimum values. If the derivative is zero along this interval, this is an inflection point.

Definition--Calculus Topics--Extreme Value Theorem Calculus Vocabulary

Definition--Calculus Topics--First Derivative

Definition--Calculus Topics--First Derivative

For differentiable function f(x), the first derivative is denoted as f'(x).

Definition--Calculus Topics--First Derivative Calculus Vocabulary

Definition--Calculus Topics--Floor Function

Definition--Calculus Topics--Floor Function

A discrete function that takes real number values and whose output is the greatest integer value greater than the input value. The graph looks like a staircase.

Definition--Calculus Topics--Floor Function Calculus Vocabulary

Definition--Calculus Topics--Fundamental Theorem of Calculus

Definition--Calculus Topics--Fundamental Theorem of Calculus

The theorem that relates differentiation and integration. The two operations are basically inverses of each other.

Definition--Calculus Topics--Fundamental Theorem of Calculus Calculus Vocabulary

Definition--Calculus Topics--Hooke's Law

Definition--Calculus Topics--Hooke's Law

A second-order differential equation that is used to model simple harmonic motion using a trigonometric function.

Definition--Calculus Topics--Hooke's Law Calculus Vocabulary

Definition--Calculus Topics--Horizontal Asymptote

Definition--Calculus Topics--Horizontal Asymptote

A horizontal line that the graph of a function approaches but does not intersect. The equation of a horizontal asymptote is y = c, for some constant c.

Definition--Calculus Topics--Horizontal Asymptote Calculus Vocabulary

Definition--Calculus Topics--Implicit Differentiation

Definition--Calculus Topics--Implicit Differentiation

When a function cannot be written in the form of y as a function of x, then implicit differentation can be used to find the derivative with respect to x.

Definition--Calculus Topics--Implicit Differentiation Calculus Vocabulary

Definition--Calculus Topics--Implicit Function

Definition--Calculus Topics--Implicit Function

A function in which y cannot be written as a function of x, where y is on the left side of the equation and all terms with x are on the right side of the equation.

Definition--Calculus Topics--Implicit Function Calculus Vocabulary

Definition--Calculus Topics--Indefinite Integral

Definition--Calculus Topics--Indefinite Integral

The integral of a function without a specific limit on the endpoints. The result of an indefinite integral is a differentiable function.

Definition--Calculus Topics--Indefinite Integral Calculus Vocabulary