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

Write a function that describes a relationship between two quantities.

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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 $f(x) *g(x)$.
1. $6x^2+x-12$
2. $6x^2-x+12$
3. $-6x^2-x-12$
4. $6x^2-x-12$
Find the domain of the composite function $f(g(x))$.

$f(x)= x+3$
$g(x)= 2/(x+6)$
1. $(-oo,3) uu (3,oo)$
2. $(-oo,oo)$
3. $(-oo,-6) uu (-6,3) uu (3,oo)$
4. $(-oo,-6) uu (-6,oo)$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let $f(x) = 5x-2 and g(x)= (3x)/ (2+x)$. Find $(g@f)(x)$.
1. $(15x)/(x+2) - 2$
2. $(15x)/(2+5x)$
3. $(3x(5x-2))/(x+2)$
4. $(15x-6)/(5x)$
Given the sequence $128, 64, 32, 16, 8, ...$ which of the following functions describes it? Assume $n in NN$.
1. $t(1) = 128; \ \ t(n) = 2 t(n-1), \ n>1$
2. $t(1) = 128; \ \ t(n) = 128 - t(n-1), \ n>1$
3. $t(1) = 128; \ \ t(n) = t(n) - 1/2t(n-1), n>1$
4. $t(1) = 128; \ \ t(n) = 1/2 t(n-1), \ n>1$
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find $(f*g)(x)$ if $f(x) = x^2 - 6x + 2$ and $g(x) = 5x-7$.
1. $5x^3 +23x^2 -32x - 14$
2. $5x^3 - 37x^2 + 52x - 14$
3. $5x^3 - 6x - 14$
4. $-32x^2 + 42x - 14$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find $(f@g)(x)$ and state its domain, if $f(x) = log(-x-5)$ and $g(x) = sqrt(x)$.
1. $log(-sqrt(x)-5), \ \ x>0$
2. $log(-sqrt(x)-5), \ \ x<0$
3. $log(-sqrt(x)-5), \ \ x>25$
4. This composite function is not possible.
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
$f(x) = sqrt(x+3)$ and $g(x)=2x$. Find $(f @ g)(4)$.
1. $2sqrt14$
2. $sqrt11$
3. $sqrt14$
4. $2sqrt7$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let $f(x) = 3x^2-5x and g(x)=sqrt(x+2)$. Find $(g@f)(x)$.
1. $3(x+2) - 5sqrt(x+2)$
2. $sqrt(3x^2-5x+2$
3. $-2x + 6$
4. $sqrt(3)x - (sqrt(5) -1) sqrt(x)$
Which of the following functions describes the sequence $18, 31/2, 13, 21/2, 8, ... ?$ Assume that $n in NN$.
1. $t(1) = 18; \ \ t(n) = 43/50 t(n-1), n>1$
2. $t(1) = 18; \ \ t(n) = t(n-1) - 5/2, n>1$
3. $t(1) = 18; \ \ t(n) = t(n-2) - 5, n>2$
4. $t(1) = 18; \ \ t(n) = 5/2 - t(n-1), t>1$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
For $f(x) = 7x^3 - 8x^2 + x - 12$ and $g(x) = -x^2 + 5x +2$, find $(f+g)(x)$.
1. $7x^3 - 7x^2 - 4x - 14$
2. $7x^3 - 8x^2 + 5x - 12$
3. $7x^3 + 9x^2 + x - 10$
4. $7x^3 - 9x^2 + 6x - 10$
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If $(f@g)(x) = x^2 + 2x + 4$, which of the following could be the functions $f(x)$ and $g(x) ?$ Choose all correct answers.
1. $f(x) = x^2 + 3, \ \ g(x) = x+1$
2. $f(x) = x + 2, \ \ g(x) = x^2 + 2x + 2$
3. $f(x) = x - 5, \ \ g(x) = x^2 + 2x + 9$
4. $f(x) = x^2 + 2, \ \ g(x) = 2x$
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 $(g + f) (x)$.
1. $-32x^4-3$
2. $12x^4 - 3$
3. $4x^2 -3$
4. $4x^4 -3$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
$f(x) =7x+9 and g(x) = 4x-1$. Find $(f @ g)(x)$.
1. $28x+8$
2. $28x+16$
3. $28x+2$
4. $28x+35$
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If $g(x) = 4/(2-x) and (g@f)(x) = -2/x^2$, find $f(x)$.
1. $(2x^2)/(x^2+1)$
2. $(x-2)/x^2$
3. $2x^2 + 2$
4. $-1/(2(x^2 - 2))$
Which of the following functions correctly describes the sequence $1,3,5,9,13,21,...?$ Assume that $n in NN$.
1. $t(1) = 1, t(2) = 3; \ \ t(n) = 2t(n-2) + 3, n>2$
2. $t(1) = 1; \ \ t(n) = t(n-1) + 2, n>1$
3. $t(1)=1, t(2)=3; \ \ t(n) = t(n-2) + t(n-1) + 1, n>2$
4. $t(1) = 1; \ \ t(n) = t(n-1) + 2^(n-1), \ n>1$
Find $(f+g)(x)$ if $f(x) = 3x^2 - 9$ and $g(x) = -7x + 1$.
1. $3x^2 - 7x - 8$
2. $3x^2 - 8$
3. $3x^2 + 7x - 10$
4. $-4x^2 - 8$