Function Operations

True or false: It is always true that  $\left(f+g\right)\left(x\right)\ =\ \left(g+f\right)\left(x\right)$ . 

• True

• False

Tags

CCSS.7.EE.A.1

If  $f\left(x\right)\ =\ -x^2+3$  and  $g\left(x\right)\ =\ x^3+2x^2-2$ , then  $\left(f-g\right)\left(x\right)\ =\ ...$   

•  $x^3+x^2+1$  

•  $x^3+3x^2-5$  

•  $-x^3-3x^2+5$  

•  $0$  

Tags

CCSS.HSF-BF.A.1B

Given $f\left(x\right)\ =\ 3x^2+x+4$ , find two non-zero functions  $g\left(x\right)$  and  $h\left(x\right)$  such that  $f\left(x\right)\ =\ \left(g-h\right)\left(x\right).$  

Let $f\left(x\right)\ =\ 2x-2x^2$ . Select all of the following ways  that  $f\left(x\right)$  can be written as a product,  $f\left(x\right)\ =\ \left(g\cdot h\right)\left(x\right)$ . 

•  $g\left(x\right)\ =\ 4$  and  $h\left(x\right)\ =\ \frac{1}{2}x-\frac{1}{2}x^2$  

•  $g\left(x\right)\ =\ x^2$  and  $h\left(x\right)\ =\ 2x-1$  

•  $g\left(x\right)\ =\ 1-x$  and  $h\left(x\right)\ =\ 2x$  

•  $g\left(x\right)\ =\ 2x-2x^2$  and  $h\left(x\right)=1$  

Let $f\left(x\right)\ =\ x^2-25$ and  $g\left(x\right)\ =\ x^2-7x+10$ . Find the quotient  $\left(\frac{g}{f}\right)\left(x\right)$  in simplified form.

Make sure you enter your answer with all necessary parentheses. For example, you could enter  $\frac{2}{x+1}$  as 2/(x+1).  
  

Tags

CCSS.HSA.APR.D.6

Select all that apply: the division of functions often results in...

• exponential growth

• a more restricted domain

• sinusoidal behavior

• vertical asymptotes

Tags

CCSS.HSF-BF.A.1B

Let $f\left(x\right)\ =\ e^x$ and  $g\left(x\right)\ =\ x^2$ . Then  $f\left(g\left(x\right)\right)\ =\ ...$   

•  $e^{x^2}$  

•  $e^{2x}$  

•  $e^xx^2$  

•  $e^2x^x$  

Tags

CCSS.HSF-BF.A.1C

Let  $f\left(x\right)\ =\ \sin\left(x\right)$ ,  $g\left(x\right)\ =\ 3x^2-1$ , and  $h\left(x\right)\ =\ 2x$ .

Find  $f\left(g\left(h\left(x\right)\right)\right)$ .  

•  $2\sin\left(3x^2-1\right)$  

•  $3\sin^2\left(2x\right)-1$  

•  $\sin\left(6x^2-2\right)$  

•  $\sin\left(12x^2-1\right)$  

Tags

CCSS.HSF-BF.A.1C

Consider the composition of four functions $f\left(x\right)\ =\ \cos^2\left(4e^x-1\right)+6$ . Which of the following choices lists the four functions from innermost to outermost?

(hint: think about order of operations!)

•  $x^2+6\ \longrightarrow\ \cos x\ \longrightarrow\ 4x\ -1\ \longrightarrow\ e^x$  

•  $4e^x\ \longrightarrow\ -1\ \longrightarrow\ 6\ \longrightarrow\cos^2x$  

•  $e^x\ \longrightarrow\ 4x-1\ \longrightarrow\ \cos x\ \longrightarrow\ x^2+6$  

•  $\cos^2x\ +6\ \longrightarrow\ 4\ \longrightarrow\ e^x\ \longrightarrow-1$  

Tags

CCSS.HSF-BF.A.1C

If  $f\left(x\right)\ =\ x+h$  and  $g\left(x\right)\ =\ x^2+\frac{3}{x}$ , then  $g\left(f\left(x\right)\right)\ =\ ...$  

•  $x^2+\frac{3}{x}+h$  

•  $x^2+h\ +\frac{3}{x}+h$  

•  $\left(x+h\right)^2-\frac{3+h}{x}$  

•  $\left(x+h\right)^2-\frac{3}{x+h}$  

Tags

CCSS.HSF-BF.A.1C