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STANDARDS

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US-VA

Math

Virginia Math

Algebra 2: Functions

A2.F.1

The student will investigate, analyze, and compare square root, cube root, rational, exponential, and logarithmic function families, algebraically and graphically, using transformations.

A2.F.1.a

Distinguish between the graphs of parent functions for square root, cube root, rational, exponential, and logarithmic function families.

A2.F.1.b

Write the equation of a square root, cube root, rational, exponential, and logarithmic function, given a graph, using transformations of the parent function, including 𝑓(𝑥) + 𝑘; 𝑓(𝑘𝑥); 𝑓(𝑥 + 𝑘); and 𝑘𝑓(𝑥), where 𝑘 is limited to rational values. Transformations of exponential and logarithmic functions, given a graph, should be limited to a single transformation.

A2.F.1.c

Graph a square root, cube root, rational, exponential, and logarithmic function, given the equation, using transformations of the parent function including 𝑓(𝑥) + 𝑘; 𝑓(𝑘𝑥); 𝑓(𝑥 + 𝑘); and 𝑘𝑓(𝑥), where 𝑘 is limited to rational values. Use technology to verify transformations of the functions.

A2.F.1.d

Determine when two variables are directly proportional, inversely proportional, or neither, given a table of values. Write an equation and create a graph to represent a direct or inverse variation, including situations in context.
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A2.F.1.e

Compare and contrast the graphs, tables, and equations of square root, cube root, rational, exponential, and logarithmic functions.

A2.F.2

The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.

A2.F.2.a

Determine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities.

A2.F.2.b

Compare and contrast the characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions.
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A2.F.2.c

Determine the intervals on which the graph of a function is increasing, decreasing, or constant.
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A2.F.2.d

Determine the location and value of absolute (global) maxima and absolute (global) minima of a function.
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A2.F.2.e

Determine the location and value of relative (local) maxima or relative (local) minima of a function.
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A2.F.2.f

For any value, 𝑥, in the domain of 𝑓, determine 𝑓(𝑥) using a graph or equation. Explain the meaning of 𝑥 and 𝑓(𝑥) in context, where applicable.
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A2.F.2.g

Describe the end behavior of a function.
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A2.F.2.h

Determine the equations of any vertical and horizontal asymptotes of a function using a graph or equation (rational, exponential, and logarithmic).

A2.F.2.i

Determine the inverse of a function algebraically and graphically, given the equation of a linear or quadratic function (linear, quadratic, and square root). Justify and explain why two functions are inverses of each other.

A2.F.2.j

Graph the inverse of a function as a reflection over the line 𝑦 = 𝑥.

A2.F.2.k

Determine the composition of two functions algebraically and graphically.