Soldan Algebra 2 Unit 5 Test

 $f\left(x\right)=x^3+3x^2+5$   $g\left(x\right)=x^3+x^2-11x-13$  
What is  $\left(f+g\right)\left(x\right)$  ?

•  $x^3+4x^2-11x-18$  

•  $x^3+3x^2-11x-18$  

•  $x^2+3x-8$  

•  $2x^3+4x^2-11x-8$  

 $f\left(x\right)=x^2-3x-5,\ \ g\left(x\right)=x^2+7x-11$  
What is  $\left(f-g\right)\left(x\right)$  ?

•  $x^2-10x+6$  
  

•  $x^2-10x-16$  
  

•  $-10x+6$  

•  $x^2+2x+1$  

Answer explanation

if you did  $-5-\left(11\right)$   you would have narrowed your choices to 2,  from there you should get it.

 $f\left(x\right)=x^2-x+5,\ \ g\left(x\right)=x^2+x+5$  
What is  $\left(f\times g\right)\left(x\right)$  ?

•  $x^4+9x^2+25$  

•  $x^4+9x^2+11x+25$  

•  $x^3-7x^2+2x+50$  
  

•  $2x^3-3x^2+7x+25$  

Answer explanation

Don't forget to take a picture of your scrap paper for your teacher after you finish your test. Your work on this problem would be great.

 $f\left(x\right)=x^2-5x-14,\ \ g\left(x\right)=x+2$  
What is  $\left(\frac{f}{g}\right)\left(x\right)$  ?

•  $x-7$  

•  $x+7$  

•  $x-7;\ x\ne2$  
  

•  $x-7;\ x\ne-2$  

 $f\left(x\right)=x^2-3x-10,\ \ g\left(x\right)=x+7$  
What is  $\left(\frac{f}{g}\right)\left(x\right)$  ?

•  $x+7$  

•  $x-5$  

•  $x+2$  

•  $\frac{x^2-3x-10}{x+7}$  

Answer explanation

If they have no common factors,  it cannot be reduced.

 $f\left(x\right)=5x-1,\ \ g\left(x\right)=x^2$  
What is  $f\left(g\left(2\right)\right)$  ?
(just write the answer nothing else)

 $f\left(x\right)=5x+1,\ \ g\left(x\right)=x^3-1$  
What is  $f\left(f\left(2\right)\right)$  ?
(just write the answer, nothing else.)

Answer explanation

The function  $g\left(x\right)\$  should have been ignored.

 $y=x^2-2$  It is a composite function.
Which is the inside function, which is the outside function?

•  $x-2$  is the inside function,   $x^2$  is the outside function

•  $x^2$  is the inside function,   $x-2$  is the outside function

•  $x^2-4\$  is the inside function   $x-2$  is the outside function.

•  $x-2$  is both the inside and outside function

The following are point on the function  $f\left(x\right)$  .   $\left(3,-7\right),\ \left(-4,-2\right),\left(1,9\right),\ \left(11,10\right)$  .  Mark all points that are on the inverse function.

•  $\left(-7,3\right)$  

•  $\left(-2,-4\right)$  

•  $\left(-9,-1\right)$  

•  $\left(11,10\right)$  

Answer explanation

Remember just reverse the  $x$ and $y$   

 $f\left(x\right)=3x+2$  
 $f^{-1}\left(x\right)$  =

•  $3x-2$  

•  $\frac{x-2}{3}$  

•  $-\frac{1}{3}\left(x+2\right)$  

•  $-3x-2$