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

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Grade 11 Function and Algebra Concepts CCSS: HSF-BF.A.1b

$f(x)=x^3+8$ and g(x)=x+2, find

$(f/g)(x)$ and its domain.

$x^2−4x+4$ ; all real numbers except x=0
$x^2+2x+2$ ; all real numbers except x=2
$x^2−2x+4$ ; all real numbers except x=-2
$x^3+4$ ; all real numbers except x=-2

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

Given

$f(x)=3x+4 and g(x)=2x-3$ , find

$f(x)+g(x)$ .

$5x+1$
$5x +7$
$x+1$
$x-1$

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

If f(x) = 2x - 1 and g(x) = 4x + 5, what is (f + g)(x)?

6x + 4
2x + 4
8x + 4
6x + 6

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

Find f/g(x) for

$f(x)=x^2−4$ and g(x)=x−2 and state its domain.

x+2; all real numbers except x=2
x-2; all real numbers except x=-2
$X^2-2$ ; all real numbers except x=0
x+4 all real numbers except x=2

Grade 11 Function and Algebra Concepts CCSS: HSF-BF.A.1b

Given

$f(x)=x^2+3x$ and g(x)=2x−1, find (f⋅g)(x).

$2x^3−x^2+3x$
$2x^3+3x^2-x$
$2x^3+5x^2-1$
$2x^3+5x^2-3x$

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

Given

$f(x)=3x+4 and g(x)=2x-3$ , find

$f(x) *g(x)$ .

$6x^2+x-12$
$6x^2-x+12$
$-6x^2-x-12$
$6x^2-x-12$

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

$f(x) = 9x^3 - 6x^2 + 10$ and

$(f+g)(x) = 9x^3 - 10x^2 - 10x + 5$ , find

$g(x)$ .

$9x^3 - 19x^2 - 4x - 5$
$-16x^2 -10x +15$
$-4x^2 - 10x - 5$
$4x^2 - 5$

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

In general, an airplane's ground speed is equal to its airspeed plus the wind speed. A certain airplane is traveling due north, and its airspeed is approximately given by the function

$A(t) = -3.515t^6 + 63.267t^5 - 445.43t^4+1549.1t^3 - 2774t^2 +2425t + 17$ ,

$\ 0.5 <= t <= 5.5$ , where

$t$ is the time in hours since it left the airport, and

$A(t)$ is measured in km/h. The wind speed during this time, which is directly in a southerly direction, is approximately modeled by the function

$W(t) = 0.0069t^6 - 0.4t^5 + 5t^4 - 24.7t^3 + 52.3t^2 - 42t + 70$ ,

$\ 0 <= t <= 6$ , where

$t$ is the time in hours since the plane left the airport, and

$W(t)$ is measured in km/h. What is the ground speed of the plane for this period of time?

$(A+W)(t) = -3.5081t^6 + 63.667t^5 - 440.43t^4 + 1573.8t^3 - 2721.7t^2 + 2467t + 87$ , $\ 0 <= t <= 6$
$(A-W)(t) = -3.5219t^6 + 62.867t^5 - 450.43t^4 + 1524t^3 - 2826.3t^2 + 2383t - 53$ , $\ 0 <= t <= 6$
$(A+W)(t) = -3.5081t^6 + 62.867t^5 - 440.43t^4 + 1524.4t^3 - 2721.7t^2 + 2383t + 87$ , $\ 0.5 <= t <= 5.5$
$(A-W)(t) = -3.5219 t^6 + 63.667t^5 - 450.43t^4 + 1573.8t^3 - 2826.3t^2 + 2467t - 53$ , $\ 0.5 <= t <= 5.5$

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

$f(x)=x^3−1$ and g(x)=x−1, find f/g(x) and its domain.

$x^2-x+1;$ all real numbers except x=-1
$x^2+x+1;$ all real numbers except x=1
x+1; all real numbers except x=0
$x^3−1;$ all real numbers except x=1

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

$f(x)=x^2−x+3$ and

$g(x)=4x^2+6x−4$ find f(x)+g(x).

$5x^2+5x−2$
$5x^2+5x−1$
$5x^2+5x+3$
$5x^2-5x+3$

Grade 11 Function and Algebra Concepts CCSS: HSF-BF.A.1b

Find

$(f/g)(x)$ if

$f(x)=x^2−4$ and g(x)=2x+1.

$(x^2+4)/(2x+1)$
$(x^2-4)/(2x+1)$
$(x^2-4x)/(2x+1)$
$(x^2-4x)/(2x)$

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

Given

$f(x)=x^2-4x+6$ and

$g(x)=7x-2$ , find

$f(x) + g(x)$ .

$x^2+3x+4$
$x^2+11x+4$
$x^2+3x+8$
$x^2-3x-8$

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

For

$f(x) = 4x-9$ and

$g(x) = 4x^2 - 5x - 9$ , find

$(f/g)(x)$ (in simplest form) and state its domain.

$1/(x+1); \ \ x !=-1, 9/4$
$(4x-9)/(4x^2 - 5x - 9); \ \ RR$
$1/(4x-9); \ \ x!= 9/4$
$1/(x+1); \ \ x!=-1$

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

A very large container has 5 gallons of water already in it and more water being added to it. The function

$W(t) = 0.05t^2 + 5, \ \ 0 <= t < 24$ describes this, where

$W$ is measured in gallons and

$t$ is measured in hours. Just as the additional water is beginning to be added, a small population of bacteria is introduced to the container. Its growth in the water can be modeled approximately by the function

$B(t) = 50e^(0.1t), \ \ t>=0$ , where

$B$ is the number of bacteria present, and

$t$ is the time, in hours. What is the approximate concentration of bacteria, in bacteria count per gallon, at a given time

$t$ as the container fills with water?

$(W*B)(t) = (0.05t^2 + 5) * (50e^(0.1t)), \ \ 0 <= t < 24$
$(W/B)(t) = (0.01t^2 + 1) / (10e^(0.1t)), \ \ 0 <= t < 24$
$(B/W)(t) = (1000e^(0.1t)) / (t^2 + 100), \ \ 0 <= t < 24$
$(B/W)(t) = (10e^(0.1t)) / (0.05t^2 + 1), \ \ 0 <= t < 24$

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

Find (f+g)(x) for

$f(x)=x^2−4x$ and

$g(x)=(2x^2−8)/(x+2$ , and its domain.

$3x^2−4x+8; x≠−2$
3x−4; R
2x+4; x≠−2
$(3x^2−8)/(x+2); x≠−2$

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

Find (f−g)(x) if f(x)=4x+3 and g(x)=2x−5.

6x−2
2x+8
2x-8
2x+2

Grade 11 Function and Algebra Concepts CCSS: HSF-BF.A.1b

Given

$f(x)=1/x$ and

$g(x)=x^2−9$ , what is

$(f/g)(x)$ and its domain?

$1/(x(x^2−9))$ ; all real numbers except x=0,±3
$(x^2−9)/x$ ; all real numbers except x=0
$1/(x^3−9)$ ; all real numbers except x=
$x(x^2−9)$ ; all real numbers

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

$g(x)= 8x^2-3$ and

$f(x)= -4x^2$ .
Find

$(g + f) (x)$ .

$-32x^4-3$
$12x^4 - 3$
$4x^2 -3$
$4x^4 -3$

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