Common Core Standard HSF-BF.A.1a Questions

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

$a(n) = 3 + 5*2^n, \ n in NN, n >=1$ , which of the following recursive formulas defines the same sequence? Assume for all sequences that

$n in NN$ .

$t(1) = 13; \ \ t(n) = 3 + 5*2^(n-1), n>1$
$t(1) = 13; \ \ t(n) = 2 t(n-1), \ n>1$
$t(1) = 13; \ \ t(n) = 13 + t(n-1), \ n>1$
$t(1) = 13; \ \ t(n) = -3 + 2t(n-1), \ n >1$

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

The values in the table below come from a quadratic function. Determine the algebraic function rule.

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ -5 \ \ \ \ \ \$	$\ \ \ \ \ \ -4 \ \ \ \ \ \$	$\ \ \ \ \ \ -3 \ \ \ \ \ \$	$\ \ \ \ \ \ -2 \ \ \ \ \ \$	$\ \ \ \ \ \ -1 \ \ \ \ \ \$
$\ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \$	$120$	$85$	$56$	$33$	$16$

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

A person saves $50 in the first week and increases their savings by $10 each week. Write a recursive function f(x) for the total savings after x weeks.

f(x)=f(x−1)+50,f(1)=10
f(x)=f(x−1)+50,f(1)=50
f(x)=f(x−1)+10,f(1)=10
f(x)=f(x−1)+10,f(1)=50

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

A student borrows $10,000 with an interest rate of 6% compounded annually. Write an explicit formula for the loan balance, B(t), after t years.

B(t)=10000(1+0.06t)
$B(t)=10000(1.06)^t$
B(t)=10000(1−0.06t)
B(t)=10000(1.06t)

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

Which of the following recursive functions defines the sequence

$5,8,11,14,... ?$ Assume

$n in NN$ .

$t(1) = 3; \ \ t(n) = t(n-1) + 5, \ n>1$
$t(1) = 5, \ \ t(n) = t(n-1) - 3, \ n>1$
$t(1) = 5, \ \ t(n) = t(n-1) + 3, \ n>1$
$t(2) = 8, \ \ t(n) = t(n-2) + 6, \ n>2$

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

The values in the table come from an exponential function of the form

$f(x) = a * e^(bx)$ , where

$a, b in RR$ . The function values in the table have been rounded to two decimal places. Find the numeric values of the coefficients

$a$ and

$b$ .

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ 0 \ \ \ \ \ \$	$\ \ \ \ \ \ 1 \ \ \ \ \ \$	$\ \ \ \ \ \ 2 \ \ \ \ \ \$	$\ \ \ \ \ \ 3 \ \ \ \ \ \$	$\ \ \ \ \ \ 4 \ \ \ \ \ \$
$\ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \$	$-3$	$-1.82$	$-1.10$	$-0.67$	$-0.41$

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

A school cafeteria serves 120 students initially and adds 8 more meals per day. Which explicit rule represents the total number of meals, M(d), after d days?

M(d)=120+8d
M(d)=8+120d
M(d)=128d
M(d)=120d−8

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

A gym charges $50 to join and $25 per month for membership. Write a function f(x) to represent the total cost after x months.

f(x)=50x+25
f(x)=50+25x
f(x)=25x−50
f(x)=50−25x

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

Given the sequence

$1,4,16,64,256,...$ , which of the following correctly defines this sequence in a recursive form? Assume that

$n in NN$ .

$t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1$
$t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1$
$t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1$
$t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1$

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

The values in the table come from either a linear, a quadratic, or an exponential function. If it is an exponential function, assume that it takes the form

$f(x) = a*e^(b x)$ , where

$a, b in RR$ . Determine the function rule that describes the data in the table. Round answers to two decimal places if necessary.

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ 10 \ \ \ \ \ \$	$\ \ \ \ \ \ 11 \ \ \ \ \ \$	$\ \ \ \ \ \ 12 \ \ \ \ \ \$	$\ \ \ \ \ \ 13 \ \ \ \ \ \$	$\ \ \ \ \ \ 14 \ \ \ \ \ \$
$\ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \$	$-5.28$	$-5.84$	$-6.4$	$-6.96$	$-7.52$

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

A water tank starts with 1,000 gallons and loses 15 gallons every day. Write a recursive formula for the amount of water left,

$w_n$ , after n days.

$W_n=W_(n-1)−15,W_0=0$
$W_n=W_(n-1)+15,W_0=1000$
$W_n=W_(n-1)−15,W_0=1000$
$W_n=W_(n-1)+15,W_0=0$

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

A certain bacteria culture doubles every 3 hours. If the initial population is 500, what will it be after 12 hours?

4,000
2,000
8,000
6,000

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

What is the function rule of the total cost T(x) of x books, if each book costs $11.95?

T(x) = 11.95x
T(x) = 11.95 - x
T(x) = x + 11.95
T(x) = x - 11.95

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

Find the recursive form of the sequence

$10, 5, 0, -5, -10,...$ Assume

$n in NN$ .

$t(1) = 10; \ \ t(n) = -t(n-1) + 5, \ n>1$
$t(1) = 10; \ \ t(n) = -5 + t(n-1), \ n>1$ .
$t(1) = 10; \ \ t(n) = 10 - t(n-1), \ n>1$ .
$t(1) = 10; \ \ t(n) = t(n-1) - 5, n>1$

Grade 11 Exponents CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2

A lab keeps blood samples in a special fridge, which is kept at 0 °C, for a certain experiment. After the blood is initially taken from a patient and put in the fridge, its temperature is checked every 30 minutes for the first two hours. Below are those recordings. Which exponential function rule best describes this information?

$\ \ \ \ \ \ \ \ \ \ \ mathbf{"Time in Fridge (min)"} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{"Temperature (°C)"} \ \ \ \ \ \ \ \ \ \$
$30$	$19.2$
$60$	$10.5$
$90$	$5.8$
$120$	$3.2$

$f(t) = 35.2 * (-0.02)^t$
$f(t) = 35.2 * 0.98^t$
$f(t) = 6.8 * 1.08^t$
There is not enough information given in the table to find the function rule.

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

A population of bacteria doubles every hour, starting with 100 bacteria. Write a function f(x) to represent the population after x hours.

$f(x)=100⋅2^x$
$f(x)=2⋅100^x$
f(x)=100+2x
$f(x)=100x^x$

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

A car loses 15% of its value each year. If its initial value is $25,000, how much is it worth after 4 years? Round to the nearest dollar.

$15,625
$16,821
$12,870
$18,100

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

What is the function rule for the given set of ordered pairs?

{(0,1), (1,-4), (2,-9), (3,-14), (4,-19)}

f(x) = x - 5
f(x) = -5x - 4
f(x) = 5x - 1
f(x) = -5x + 1

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

Given the sequence

$128, 64, 32, 16, 8, ...$ which of the following functions describes it? Assume

$n in NN$ .

$t(1) = 128; \ \ t(n) = 2 t(n-1), \ n>1$
$t(1) = 128; \ \ t(n) = 128 - t(n-1), \ n>1$
$t(1) = 128; \ \ t(n) = t(n) - 1/2t(n-1), n>1$
$t(1) = 128; \ \ t(n) = 1/2 t(n-1), \ n>1$

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Common Core Standard HSF-BF.A.1a Questions

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