Common Core Standard HSF-BF.A.1 Questions

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Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a

A car rental company charges a $25 base fee and $0.15 per mile driven. Write a function f(m) to represent the total cost for driving m miles.

f(m)=25+0.15
f(m)=25m+0.15
f(m)=25+0.15m
f(m)=0.15m−25

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a

A movie streaming service charges $8 per month plus $2 per movie rented. Write a function f(x) for the total monthly cost if x movies are rented.

f(x)=8+2x
f(x)=2+8x
f(x)=8x−2
f(x)=2x−8

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Given

$(f∘g)(x)=4x^2−12x+9$ , which pair could be f and g?

$f(x)=2x−3 , g(x)=x^2$
$f(x)=x^2 , g(x)=2x-3$
$f(x)=4x+9 , g(x)=2x^2-3x$
$f(x)=2x−3 , g(x)=4x^2-12x+9$

Grade 9 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a

A student collecting money for a charity is donating $12 of his own money. He asks friends to give $5 each. Write a rule in function notation to find how much he will donate in all. Let p represent then number of friends who give money.

$f(p)=12p+5$
$f(p)=12+5p$
$f(p)=12+5+p$
$f(p)=17p$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$f(x) = sqrt(x+8) and g(x)= 8x-12$ . Find

$(f @ g)(x)$ .

$2sqrt(2x-1)$
$8sqrt(x+8)-12$
$8sqrt(x-4)$
$2sqrt(2x+1)$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Let

$f(x) = x^2 + 6 and g(x) = (x+8)/x.$ Find

$(g@f) (-7)$ .

-55/7
384/7
295/49
63/55

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Let

$f(x) = 5x-1 and g(x) = 3x^2 + 2x - 1$ . Find

$(g@f)(x)$ .

$75x^2 - 20x$
$15x^2+10x-6$
$75x^2-28x+2$
$25x-3$

Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2

Given the sequence

$1, -3, -9, -17, -27, ...$ , which of the following functions correctly describes it? Assume that

$n in NN$ .

$t(1) = 1, t(2) = -3; \ \ t(n) = t(n-1) - 6t(n-2), n>2$
$t(1) = 1; \ \ t(n) = t(n-1) -4, \ n>1$
$t(1) = 1; \ \ t(n) = t(n-1) - 2n, \ n > 1$
$t(1) = 1; \ \ t(n) = (-1)^(n-1) * 3 * t(n-1), n>1$

Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b

Find

$f(x)$ if

$g(x) = 3x-1$ and

$(f*g)(x) = 6x^2 + 10x - 4$ .

$f(x) = x-2$
$f(x) = 2x + 10/3$
$f(x) = x+2$
$f(x) = 2x+4$

Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b

A small town is growing. Its population is increasing and its borders are expanding. The town's population growth can be modeled by the function

$P(t) = 100e^(0.8t)$ , where

$t$ is the number of years that have passed since the current date and

$P$ is the approximate number of people living in the town. The land area of the town can be approximately modeled by the function

$A(t) = 0.25 pi (1+t)^2$ , where

$t$ is the number of years since the current date and

$A$ is the land area in square kilometers. Which combined function shows the population density of the town?

$(P/A)(t) = (100e^(0.8t)) / (0.25 pi (1+t)^2)$
$(A/P)(t) = (0.25 pi (1+t)^2) / (100e^(0.8t))$
$(A/P)(t) = 100e^( (0.8t) / (0.25 \ pi \ (1 \ + \ t)^2))$
$(A*P)(t) = 25 pi e^(0.8t) (1+t)^2$

Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$(f@g)(x) = 10x - 2$ , which of the following are possible function rules for

$f(x)$ and

$g(x) ?$ Choose all correct answers.

$f(x) = 10x + 10, \ \ g(x) = x - 12$
$f(x) = 2x-4, \ \ g(x) = 5x+1$
$f(x) = 8x-9, \ \ g(x) = 5/4 x - 11/4$
$f(x) = 1/2x - 3 \ \ g(x) = 20x + 2$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a

An investment of $1,000 grows by 5% each year. Write a recursive rule for the total value,

$V_n$ , after n years.

$V_n=1.05V_(n-1),V_0=0$
$V_n=1.05V_(n-1),V_0=1000$
$V_n=V_(n-1)+0.05,V_0=1000$
$V_n=1.5V_(n-1),V_0=1000$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a

A population of 1,000 increases by 8% each year. How large will the population be after 5 years? Round to the nearest whole number.

1,360
1,469
1,520
1,700

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a

What is the function rule for the total cost, T(x), of x apples, if each apple costs $0.75?

T(x)=0.75x
T(x)=0.75+x
T(x)=0.75−x
T(x)=x−0.75

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$f(x)=1/x$ and g(x)=x−5, find (f∘g)(2).

$-1/3$
$1/3$
-3
3

Grade 11 Functions and Relations CCSS: HSF-IF.A.2, HSF-BF.A.1, HSF-BF.A.1c

For x = -2, evaluate f(g(x)) - f(0), given that:

$f(x) = 2x + 5$

$g(x) = 4x$

-11
6
-4
-16

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$f(x) = 3x-12 and g(x) = 4x$ . Find

$(f @ g)(x)$ .

$12x^2+48x$
$12x-48$
$12x-12$
$7x-12$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b

Let

$f(x)=3x +2 and g(x)=7x +6$ . Find

$(f*g)(x)$ .

$6x^2 +4x +42$
$6x^2 +4x +56$
$21x^2 +32x +12$
$21 x^2 + 32x +24$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

For

$f(x) = 3x^2 - 1$ and

$g(x) = sqrt(2x-5)$ , find

$(g@f)(x)$ .

Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a

Which of the function rules describes the data in the table below?

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ -2 \ \ \ \ \ \$	$\ \ \ \ \ \ -1 \ \ \ \ \ \$	$\ \ \ \ \ \ 0 \ \ \ \ \ \$	$\ \ \ \ \ \ 1 \ \ \ \ \ \$	$\ \ \ \ \ \ 2 \ \ \ \ \ \$
$\ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \$	$8$	$1$	$0$	$5$	$16$

$f(x) = -x + 6$
$f(x) = 3x^2 + 2x$
$f(x) = 5x^2 + 6x$
$f(x) = 134 e^(0.0036x)$

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