Algebra 2 Quarter 2 Review

Algebra 2 Quarter 2 Review

Properties of Polynomial Functions

Multiple Choice

Problem 1: Choose the correct end behavior for the function

 $f\left(x\right)=-\frac{3}{5}x^3+8x^2-5x$  

Multiple Choice

Problem 2: 

Choose the correct end behavior for the function

 $f(x)=x^8-x^2+9x+1$  

Multiple Choice

Problem 3:

Which is a possible equation for the graph shown here?

• $g(x)=x(x-2)(x+2)$

• $g(x)=x^2(x-2)(x+2)$

• $g(x)=-x^3(x+2)(x+2)$

• $g(x)=-x(x-2)(x-2)$

Multiple Choice

Problem 4: Which is a possible equation for the graph shown here?

• $f(x)=(x-4)^2(x-1)^3(x+1)$

• $f(x)=-(x-4)^2(x-1)^3(x+1)$

• $f(x)=(x+4)^2(x+1)^3(x-1)$

• $f(x)=-(x+4)^2(x+1)^3(x-1)$

Multiple Select

Problem 5: What are the zeros of this function? Select all that apply.

 $f(x)=-3x(2x+1)(x-6)$  

•  $x=3$  

•  $x=-\frac{1}{2}$  

•  $x=6$  

•  $x=0$  

•  $x=-1$  

Multiple Select

Problem 5b: HONORS ONLY What are the zeros of this function? Select all that apply.

 $f(x)=(x-7)^3(x^2+4)$  

•  $x=-7$  

•  $x=7$  

•  $x=-4$  

•  $x=2i$  

•  $x=-2i$  

Applications of Polynomials

go to desmos.com/calculator to answer these questions

Multiple Choice

Problem 6: The profit P (in millions of dollars) for a manufacturer of MP3 players can be modeled by 

 $P(x)=-4x^3+12x^2+16x$   where x is the number of MP3 players produced (in millions).

The manufacturer hopes to make a profit of at least $26 million by the time they sell 1 million MP3 players.

Will they meet their goal?

• Yes

• No

We can see that they reach a profit of 26 million AFTER they have sold 1 million MP3 players.

Multiple Choice

Problem 7: 

The profit P (in millions of dollars) for a manufacturer of MP3 players can be modeled by 

 $P(x)=-4x^3+12x^2+16x$   where x is the number of MP3 players produced (in millions).

When will the company break even (have a profit of zero)?

• 1.01 million MP3 players

• 4 million MP3 players

• 3.6 million MP3 players

• 2.5  million MP3 players

The profit is 0 when the graph touches the x axis.

Exponential Functions

Graphs and Solving

Multiple Choice

Problem 8: The exponential function  $h\left(x\right)$ has the following characteristics:
·     $h\left(x\right)$ represents exponential growth
·     There is a horizontal asymptote at   $y=-5$  
·      The y-intercept is  $\left(0,\ 2\right)$  

Which of the following is a possible equation for  $h\left(x\right)$ ?

•  $h(x)=2(3)^x-5$  

•  $h(x)=7(1.04)^x-5$  

•  $h(x)=2\left(\frac{2}{3}\right)^x+5$  

•  $h(x)=7\left(\frac{2}{3}\right)^x-5$  

Multiple Choice

Problem 9: Which of the following statements is true for the function  $f(x)=3^{x+2}-1$  

• There is a vertical asymptote at x = 2

• There is a vertical asymptote at x = -2

• There is a horizontal asymptote at y = 1

• There is a horizontal asymptote at y = -1

Multiple Choice

Problem 10: Solve the equation for x $2\cdot4^{x-3}=128$  

• x = 6

• x = 3

• x = 0

• x = 4

Applications of Exponential Functions

for the next question open desmos.com/calculator

Multiple Choice

Problem 11: The population of a gold mining town out west between the years 1850 and 1900 is modeled by the function $P(t)=4.7(1.06)^t$  

Where $P\left(t\right)$  is the total population, in thousands, at a given time and  $t$  is the number of years since 1850.   

 Based on this model, by the beginning of which year will the population exceed 20 thousand?
 

• 1874

• 1875

• 1876

• 1877

Round the x value up to 25 years since 1850. This puts us in 1875.

Basics of Logarithms

evaluating and rewriting

Multiple Choice

Problem 12: Evaluate the expression $\log_314$  

• 0.416

• 0.669

• 2.402

• 3.438

Multiple Choice

Problem 13: Re-express the logarithmic function in exponential form $\log_3x=4$  

•  $3^x=4$  

•  $x^4=3$  

•  $3^4=x$  

•  $4^3=x$