Call Now to Set Up Tutoring:

(888) 888-0446

HiSET: Math : Functions and function notation

Study concepts, example questions & explanations for HiSET: Math

Create An Account

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Functions And Function Notation

Define $f(x)= -\frac{1}{x+1}$ and g(x) = |x+2| .

Evaluate $(f\circ g )(2)$ .

Possible Answers:

The expression is undefined.

$\frac{1}{3}$

$-\frac{1}{4}$

$- \frac{1}{5}$

Correct answer:

$- \frac{1}{5}$

Explanation:

By definition,

$(f\circ g )(2) = f(g(2))$ ,

so first, evaluate g(2) by substituting 2 for in g(x) :

g(x) = |x+2|

g(2) = |2+2| = |4| =4

$(f\circ g )(2) = f(4)$ ,

so evaluate f(4) through a similar substitution:

$f(x)= -\frac{1}{x+1}$

$f(4)= -\frac{1}{4+1} = - \frac{1}{5}$ ,

the correct response.

Report an Error

Example Question #1 : Functions And Function Notation

Define functions and as follows:

$f(x)= \left\{\begin{matrix} x^{2} -2,&x< 0 \\ x+ 3,& x \ge 0\end{matrix}\right.$

g(x)= x+ 4

Evaluate $(f \circ g)(0)$ .

Possible Answers:

Undefined

Correct answer:

Explanation:

By definition, $(f \circ g)(0) = f(g(0))$ . Evaluate g(0) by substituting 0 for in the definition of :

g(x)= x+ 4

g(0)= 0+ 4= 4

$(f \circ g)(0) = f(g(0)) = f(4)$ , so substitute 4 for in the definition of . Since 4 satisfies the condition $x \ge 0$ , use the definition for those values:

f(x)= x+ 3

f(4)= 4+ 3 = 7 ,

the correct value.

Report an Error

Example Question #1 : Functions And Function Notation

Consider the scenario below:

Helen is a painter. It takes her 3 days to make each painting. She has already made 6 paintings. Which of the following functions best models the number of paintings she will have after days?

Possible Answers:

f(x)=x-3

f(x)=3x

f(x)=6x^3

$f(x)=\frac{x}{3} +6$

f(x)=3x+6

Correct answer:

$f(x)=\frac{x}{3} +6$

Explanation:

The question asks, "Which of the following functions best models the number of paintings she will have after days?"

From this, you know that the variable represents the number of days, and that f(x) represents the number of paintings she makes as a function of days spent working.

If it takes 3 days to make a painting, each day results in $\frac{1}{3}$ paintings. Therefore, we have a linear relationship with slope $\frac{1}{3}$ .

Additionally, she begins with 6 paintings. Therefore, even when zero days are spent working on paintings, she will have 6 paintings. In other words, f(0)=6 . This means the y-intercept is 6.

As a result, the function will be

$f(x)=\frac{1}{3}x +6$

which can be rewritten as

$f(x)=\frac{x}{3} +6$

Report an Error

Example Question #2 : Interpret Statements That Use Function Notation In Terms Of A Context

The daily pay in U.S. Dollars for a certain job is defined as the following function f(x) , where equals time in hours:

f(x) = 15x+10

If an employee works for 7 hours in a day, how much is he or she paid?

Possible Answers:

$\$70.00$

$\$25.00$

$\$85.00$

$\$105.00$

$\$115.00$

Correct answer:

$\$115.00$

Explanation:

f(x) = 15x+10

The above function can be understood as, "An employee is paid $15 for each hour he or she works, plus a flat amount of $10."

If an employee works 7 hours, we can find the amount that he or she is paid by plugging in 7 for "Hours" in the equation:

f(x)= 15(7)+10

Adhering to order of operations, we next find the product of 15 and 7:

f(x) = 105+10

Finally, we find the sum of 105 and 10:

f(x) = 115

The employee is paid $115.00 for seven hours' work.

Report an Error

Example Question #1 : Write A Function That Describes A Relationship Between Two Quantities

f(x) is a linear function defined on the set of real numbers. Four values of are given in the following table:

$\begin{matrix} \underline{x}& \underline{f(x)} \\ 13 & 4 \\ 10 & 6 \\ 7 & 8 \\ 4 & 10 \end{matrix}$

Give the definition for f(x) .

Possible Answers:

$f(x) = -\frac{3}{2} x+19$

$f(x) = -\frac{2}{3} x+14$

f(x) = 2x + 5

f(x) = -2x + 24

$f(x) = \frac{3}{2} x-11$

Correct answer:

$f(x) = -\frac{3}{2} x+19$

Explanation:

By the two-point formula, the equation of a line through points $(x_{1}, y_{1}), (x_{2}, y_{2})$ is

$y-y_{1} = m(x- x_{1})$ ,

where $m = \frac{x_{2}-x_{1}}{y_{2}-y_{1}}$ , the slope of the line. The choice of the two points from the given four is arbitrary, so we will select the middle two ordered pairs. Substituting $x_{1}= 10,y_{1} =6, x_{2}= 7, y_{2}= 8$ , then

$m = \frac{x_{2}-x_{1}}{y_{2}-y_{1}}= \frac{7-10}{8-6} = -\frac{3}{2}$

The first formula becomes

$y-10 = -\frac{3}{2}(x-6)$

Since f(x)= y , solve for . First, distribute $-\frac{3}{2}$ throughout the difference at right:

$y-10 = -\frac{3}{2} x- \left (-\frac{3}{2} \right )6$

$y-10 = -\frac{3}{2} x- \left (-9 \right )$

$y-10 = -\frac{3}{2} x+9$

Isolate by adding 10 to both sides:

$y-10+ 10 = -\frac{3}{2} x+9+ 10$

$y = -\frac{3}{2} x+19$

Replacing, the definition of f(x) is

$f(x) = -\frac{3}{2} x+19$ .

Report an Error

Example Question #1 : Domain And Range Of A Function

Define functions $f(x) = \sqrt{x}$ and $g(x) =- x^{2}$

Give the domain of the composition $g\circ f$ .

Possible Answers:

$\left ( 0, \infty\right )$

$\left [ 0, \infty\right )$

$\left ( - \infty, 0 \right ]$

$\left ( - \infty, 0 \right )$

None of the other choices gives the correct response.

Correct answer:

$\left [ 0, \infty\right )$

Explanation:

The domain of the composition of functions $g\circ f$ is that the set of all values that fall in the domain of such that f(c) falls in the domain of .

$f(x) = \sqrt{x}$ , a square root function, whose domain is the set of all values of that make the radicand nonnegative. Since the radicand is itself, the domain of is simply the set of all nonnegative numbers, or $\left [ 0, \infty\right )$ .

$g(x) =- x^{2}$ , a polynomial function, whose domain is the set of all real numbers. Therefore, the domain is not restricted further by . The domain of $g\circ f$ is $\left [ 0, \infty\right )$ .

Report an Error

Example Question #2 : Domain And Range Of A Function

Define functions $f(x) = \frac{1}{x-1}$ and $g(x)= \sqrt{x}+ 1$ .

Give the domain of the composition $g\circ f$ .

Possible Answers:

$(0, 1) \cup (1, \infty)$

$(-\infty, 1)$

(0, 1)

$(1, \infty)$

$(-\infty, 1) \cup (1, \infty)$

Correct answer:

$(1, \infty)$

Explanation:

The domain of the composition of functions $g\circ f$ is that the set of all values that fall in the domain of such that f(c) falls in the domain of .

$f(x) = \frac{1}{x-1}$ , a rational function, so its domain is the set of all numbers except those that make its denominator zero. x-1= 0 if and only if x= 1 , making its domain $(-\infty, 1) \cup (1, \infty)$ .

$g(x)= \sqrt{x}+ 1$ , a square root function, so the domain of is the set of all values that make the radicand a nonnegative number. Since the radicand is itself, the domain of is simply the set of all nonnegative numbers, or $\left [ 0, \infty\right )$ .

Therefore, we need to further restrict the domain to those values in $(-\infty, 1) \cup (1, \infty)$ that make

$f(c) \ge 0$

Equivalently,

$\frac{1}{c-1}\ge 0$

Since 1 is positive, and the quotient is nonnegative as well, it follows that

c-1 > 0 ,

and

c > 1 .

The domain of $g\circ f$ is therefore $(1, \infty)$ .

Report an Error

Example Question #5 : Functions And Function Notation

Define functions $f(x) = x^{2}-16$ and $g(x) = \sqrt{x}$ .

Give the domain of the composition $g\circ f$ .

Possible Answers:

$(-\infty, -4]$

$[4 , \infty)$

[-4, 4 ]

$(-\infty, -4] \cup [4 , \infty)$

$(-\infty, \infty)$

Correct answer:

$(-\infty, -4] \cup [4 , \infty)$

Explanation:

The domain of the composition of functions $g\circ f$ is that the set of all values that fall in the domain of such that f(c) falls in the domain of .

$f(x) = x^{2}-16$ , a polynomial function, so its domain is the set of all real numbers.

$g(x) = \sqrt{x}$ , so the domain of is the set of all values that make the radicand a nonnegative number. Since the radicand is itself, the domain of is simply the set of all nonnegative numbers, or $\left [ 0, \infty\right )$ .

Therefore, the domain of $g\circ f$ is the set of all real numbers such that

$f(c) \ge 0$ .

Equivalently,

$c^{2}-16 \ge 0$

To solve this, first, solve the corresponding equation:

$c^{2}-16 = 0$

Factor the polynomial at left using the difference of squares pattern:

(c+4)(c-4) = 0

By the Zero Factor Property, either

c+ 4 = 0 , in which case c= -4 ,

c- 4 = 0 , in which case c= 4 .

These are the boundary values of the intervals to be tested. Choose an interior value of each interval and test it in the inequality:

$(-\infty, -4)$

Testing c= -5 :

$(-5)^{2}-16 \ge 0$

$25-16 \ge 0$

$9 \ge 0$ - True; include

( -4, 4 )

Testing c= 0 :

$0^{2}-16 \ge 0$

$0 -16 \ge 0$

$-16 \ge 0$ - False; exclude

$( 4 , \infty)$

Testing c= 5 :

$5^{2}-16 \ge 0$

$25-16 \ge 0$

$9 \ge 0$ - True; include

Include $(-\infty, -4)$ and $( 4 , \infty)$ . Also include the boundary values, since equality is included in the inequality statement ( $\ge$ ).

The correct domain is $(-\infty, -4] \cup [4 , \infty)$ .

Report an Error

Example Question #1 : Functions And Function Notation

Define functions $f(x) = x^{2}-16$ and $g(x) = \sqrt{x}$ .

Give the domain of the composition $f \circ g$ .

Possible Answers:

$\left [ -4, \infty\right )$

$\left [ 0, \infty\right )$

[ -4,4]

$\left ( -\infty, \infty\right )$

$\left [ 4, \infty\right )$

Correct answer:

$\left [ 0, \infty\right )$

Explanation:

The domain of the composition of functions $f \circ g$ is the set of all values that fall in the domain of such that g(c) falls in the domain of .

$g(x) = \sqrt{x}$ , a square root function, so the domain of is the set of all values that make the radicand a nonnegative number. Since the radicand is itself, the domain of is simply the set of all nonnegative numbers, or $\left [ 0, \infty\right )$ .

$f(x) = x^{2}-16$ , a polynomial function; its domain is the set of all reals, so it does not restrict the domain any further.

The correct domain is $\left [ 0, \infty\right )$ .

Report an Error

Example Question #1 : Functions And Function Notation

Define functions $f(x) = \frac{1}{x-1}$ and $g(x)= \sqrt{x}+ 1$ .

Give the domain of the composition $f \circ g$ .

Possible Answers:

$\left (1, \infty\right )$

$\left [ 1, \infty\right )$

$\left ( -\infty, \infty\right )$

$\left [ 0, \infty\right )$

$\left ( 0, \infty\right )$

Correct answer:

$\left ( 0, \infty\right )$

Explanation:

The domain of the composition of functions $f \circ g$ is the set of all values that fall in the domain of such that g(c) falls in the domain of .

$f(x) = \frac{1}{x-1}$ , a rational function, so its domain is the set of all numbers except those that make its denominator zero. x-1= 0 if and only if x= 1 , so from $\left [ 0, \infty\right )$ , we exclude only the value so that

g(c) = 1 ;

that is,

$\sqrt{c}+ 1 = 1$

$\sqrt{c}+ 1 - 1 = 1 - 1$

$\sqrt{c} = 0$

c= 0

Excluding this value from the domain, this leaves $\left ( 0, \infty\right )$ as the domain of $f \circ g$ .

Report an Error

View Tutors

Margaret
Certified Tutor

Smith College, Bachelor of Science, Biological and Physical Sciences.

View Tutors

Samir
Certified Tutor

University of South Florida-Main Campus, Master of Fine Arts, Studio Arts.

View Tutors

Grace
Certified Tutor

University of Massachusetts-Dartmouth, Bachelor of Education, Portuguese. University of Massachusetts-Dartmouth, Masters in B...

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Chicago, Spanish Tutors in Houston, ISEE Tutors in Houston, Calculus Tutors in Miami, Math Tutors in Dallas Fort Worth, Biology Tutors in Atlanta, Biology Tutors in Boston, LSAT Tutors in San Francisco-Bay Area, MCAT Tutors in Seattle, Reading Tutors in Miami

Popular Courses & Classes

ISEE Courses & Classes in San Diego, Spanish Courses & Classes in Chicago, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Denver, GMAT Courses & Classes in San Diego, SAT Courses & Classes in Houston, GRE Courses & Classes in Miami

Popular Test Prep

ISEE Test Prep in Los Angeles, SSAT Test Prep in New York City, GRE Test Prep in Houston, MCAT Test Prep in Washington DC, GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Miami, LSAT Test Prep in Atlanta, ISEE Test Prep in Denver, ACT Test Prep in New York City, MCAT Test Prep in Houston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

HiSET: Math : Functions and function notation

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #1 : Functions And Function Notation

Example Question #1 : Functions And Function Notation

Example Question #1 : Functions And Function Notation

Example Question #2 : Interpret Statements That Use Function Notation In Terms Of A Context

Example Question #1 : Write A Function That Describes A Relationship Between Two Quantities

Example Question #1 : Domain And Range Of A Function

Example Question #2 : Domain And Range Of A Function

Example Question #5 : Functions And Function Notation

Example Question #1 : Functions And Function Notation

Example Question #1 : Functions And Function Notation

All HiSET: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: