Topics
5. Rational Functions
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United States of AmericaVirginia
Algebra 2

5.01 Rational parent functions

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Which of the following graphs shows the function $f\left(x\right)=\frac{1}{x}$f(x)=1x​?

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A

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B

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C

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D

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E

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F
Easy
< 1min

Consider the function in the graph.

Which one of the following could be the equation of the function?

Easy
< 1min

What family does the following function belong to?

Easy
< 1min

Consider the graphs of $f\left(x\right)=\frac{3}{x}$f(x)=3x​ and $g\left(x\right)$g(x).

Easy
1min
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Outcomes

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.1a

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

A2.F.1b

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.1c

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.1e

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.2a

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

A2.F.2b

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

A2.F.2c

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

A2.F.2f

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.

A2.F.2g

Describe the end behavior of a function.

A2.F.2h

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

A2.F.2j

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

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