TCAP High School (EOC courses) Functions Practice

What the test measures

Functions skills

HSF.IF.1 Understand that a function from one set to another assigns to each element of the domain exactly one element of the codomain
HSF.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation
HSF.IF.3 Recognize that sequences are functions
HSF.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities
HSF.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes
HSF.IF.6 Calculate and interpret the average rate of change of a function
HSF.IF.7 Graph functions expressed symbolically and show key features graphically
HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function
HSF.IF.9 Compare properties of two functions each represented in different ways
HSF.BF.1 Write a function that describes a relationship between two quantities
HSF.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula
HSF.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and combinations of such transformations
HSF.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions
HSF.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs
HSF.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly
HSF.LE.4 For exponential models, express as a logarithm the solution to ab^ct = d
HSF.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle
HSF.TF.2 Explain how the unit circle in the coordinate plane enables trigonometric functions to be extended to all real numbers
HSF.TF.3 Use special triangles to determine geometric properties of the unit circle
HSF.TF.4 Use the unit circle to explain symmetry and periodicity of trigonometric functions
HSF.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline
HSF.TF.6 Choose trigonometric functions to model periodic phenomena and fit a model to data

Standards basis

Tennessee Academic Standards for Mathematics — Tennessee

How the TCAP reports it

TCAP math is Tennessee’s state assessment program and its blueprints are aligned to Tennessee Academic Standards, which closely mirror the Common Core content structure in grades 3-8 and the CCSS-style high school conceptual categories. The blueprint page lists the current 2025-26 assessment overviews, including Math Grade 2, Grades 3-5, Grades 6-8, and Math EOC. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Blueprint & weighting

Published TCAP math blueprints assign content emphasis by grade/course, but the exact percentage table was not recoverable from the accessible blueprint page in this session. The state blueprint landing page confirms the math overviews but did not expose the PDF links in the fetched page content. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Official sources

Tennessee Department of Education TCAP Blueprints
Tennessee Education Glossary (academic standards entry)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playmedium

The first five terms of an arithmetic sequence are $25, 22, 19, 16, 13$ . What is the $15$ th term?

The common difference is $d = -3$ . With $a_1 = 25$ , the $15$ th term is $a_{15} = 25 + 14(-3) = -17$ .

Practice playeasy

Convert $\dfrac{\pi}{6}$ to degrees.

$\dfrac{\pi}{6} \times \dfrac{180°}{\pi} = 30°$ .

Practice playeasy

The function $f$ is defined by $f(x) = -3x + 22$ . What is the value of $f(x)$ when $x = 5$ ?

Substitute $x = 5$ : $f(5) = -3(5) + 22 = -15 + 22 = 7$ .

Practice playeasy

The function $f$ is defined by $f(x) = x^2 + 3$ . What is the value of $f(x)$ when $x = 4$ ?

Substitute $x = 4$ : $f(4) = 4^2 + 3 = 16 + 3 = 19$ .

Practice playeasy

For the function $f$ , $f(0) = 250$ . For each increase in $x$ by $1$ , the value of $f(x)$ decreases by $40\%$ . What is the value of $f(2)$ ?

Each step multiplies by $1 - 0.40 = 0.60$ . So $f(2) = 250 \cdot 0.60^2 = 250 \cdot 0.36 = 90$ .

Practice playeasy

$s = 18 - \dfrac{n}{2}$

The equation shown gives the estimated snow depth $s\textsf{,}$ in inches, remaining on a trail $n$ days after a storm, where $0 \le n \le 24\textsf{.}$ What is the estimated snow depth, in inches, remaining on the trail $10$ days after the storm?

Substitute $n = 10\textsf{:}$ $s = 18 - \dfrac{10}{2} = 18 - 5 = 13\textsf{.}$ The estimated snow depth remaining is $13$ inches.

Practice playeasy

The function $S$ is defined by $S(t) = 450(0.85)^{t/3}$ . The function $S$ models the height, in centimeters, of a snowpack, where $t$ is the number of days after a winter storm. According to the model, what is the estimated height, in centimeters, of the snowpack $3$ days after the storm?

When $t = 3$ , the exponent is $3/3 = 1$ . So $S(3) = 450(0.85)^1 = 382.5$ centimeters.

Practice playeasy

A substance has a half-life of $1$ years. What fraction remains after $2$ years?

$2 \div 1 = 2$ half-lives. Remaining: $\left(\dfrac{1}{2}\right)^{2} = \dfrac{1}{4}$ .

Related Common Core standards

HSF.BF.A.2 HSF.TF.A.1 HSF.IF.A.2 HSF.LE.A.2 HSF.IF.C.7 HSF.BF.B.3 HSF.TF.B.6 HSF.IF.B.4

Functions in other TCAP grades

Grade 8

Source and test overview

All TCAP prep Official test source

Reporting categories

More High School (EOC courses) domains

Number and QuantityExtend the real number system to include rational and irrational numbers, work with quantities, units, and complex numbers, and use the structure of expressions involving quantities.8 QsPractice →AlgebraSee structure in expressions, write expressions in equivalent forms to solve problems, and analyze, solve, and prove equations and inequalities.8 QsPractice →GeometryProve theorems about lines and angles, triangles, circles, and similarity; connect geometric and algebraic reasoning; and solve problems with geometric measurement and coordinate geometry.8 QsPractice →Statistics and ProbabilitySummarize, represent, and interpret data; make inferences and justify conclusions from sample surveys, experiments, and observational studies; understand conditional probability and use probability to make decisions.8 QsPractice →

TCAP High School (EOC courses) Functions. Practice it free.

Functions skills

HSF.IF.1 Understand that a function from one set to another assigns to each element of the domain exactly one element of the codomain

HSF.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation

HSF.IF.3 Recognize that sequences are functions

HSF.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities

HSF.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes

HSF.IF.6 Calculate and interpret the average rate of change of a function

HSF.IF.7 Graph functions expressed symbolically and show key features graphically

HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function

HSF.IF.9 Compare properties of two functions each represented in different ways

HSF.BF.1 Write a function that describes a relationship between two quantities

HSF.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula

HSF.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and combinations of such transformations

HSF.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions

HSF.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs

HSF.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly

HSF.LE.4 For exponential models, express as a logarithm the solution to ab^ct = d

HSF.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle

HSF.TF.2 Explain how the unit circle in the coordinate plane enables trigonometric functions to be extended to all real numbers

HSF.TF.3 Use special triangles to determine geometric properties of the unit circle

HSF.TF.4 Use the unit circle to explain symmetry and periodicity of trigonometric functions

HSF.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline

HSF.TF.6 Choose trigonometric functions to model periodic phenomena and fit a model to data

Topics mapped to this domain

Arithmetic sequence nth term

Degree-radian conversion

Evaluating functions

Evaluating functions at a value

Evaluating functions from percent change

Evaluating functions in context

Exponential functions in context (SAT)

Exponential and log formulas

Factored polynomial x-intercepts (SAT)

Function table composition (ACT)

Function transformation descriptions

Function transformations

8 free questions · 0/0 correct

Turn functions into game time.

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