Topics
1. Analyzing Functions
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United States of AmericaVirginia
Algebra 2

1.01 Characteristics of functions

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the curve on the graph below.

Loading Graph...
A parabola on a number plane that opens upward with a vertex at $\left(-4,-2\right)$(−4,−2). The coordinates of the vertex are not explicitly given.
a

State the domain of the function using interval notation.

b

State the range of the function using interval notation.

Easy
1min

The function $f\left(x\right)=\sqrt{x+1}$f(x)=√x+1 has been graphed.

Easy
1min

The graph of $y=2^x$y=2x is displayed here.

Medium
2min

A graph of the function $y=\log_2x+5$y=log2​x+5 is shown below.

Medium
1min
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Outcomes

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.2d

Determine the location and value of absolute (global) maxima and absolute (global) minima of a function.

A2.F.2e

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

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).

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