Pre Calculus Quarter 2 Review

Pre Calculus Quarter 2 Review

Unit 3 - Rational Functions

Finding all asymptotes, holes, and intercepts

Multiple Choice

Completely factor the rational function: $f\left(x\right)=\frac{x-3}{2x^2+9x+10}$  

•  $f\left(x\right)=\frac{\left(x-3\right)}{\left(2x+9\right)\left(x+10\right)}$  

•  $f\left(x\right)=\frac{\left(x-3\right)}{\left(x+1\right)\left(x+10\right)}$  

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

Multiple Select

Given the factored function $f\left(x\right)=\frac{\left(x-3\right)}{\left(x+2\right)\left(2x+5\right)}$ select all that apply.

• This function has no holes.

• This function has 1 vertical asymptote.

• This function has 1 x-intercept.

• This function has 2 vertical asymptotes

• This function has 1 hole.

Multiple Choice

Given the factored function $f\left(x\right)=\frac{\left(x-3\right)}{\left(x+2\right)\left(2x+5\right)}$ what is the x-intercept?

•  $\left(-2,\ 0\right)$  
  

•  $\left(-3,\ 0\right)$  

•  $\left(3,\ 0\right)$  

•  $\left(-\frac{5}{2},\ 0\right)$  

Multiple Select

Given the factored function $f\left(x\right)=\frac{\left(x-3\right)}{\left(x+2\right)\left(2x+5\right)}$ where are the vertical asymptotes? Select all the apply

•  $x=-2$  
  

•  $x=3$  

•  $x=-\frac{5}{2}$  

•  $x=-5$  

Multiple Choice

What is the horizontal asymptote of the function: $f\left(x\right)=\frac{x-3}{2x^2+9x+10}$  

•  $y=0$  

•  $y=\frac{1}{2}$  

• There is no horizontal asymptote

Multiple Choice

What is the y-intercept of the function: $f\left(x\right)=\frac{x-3}{2x^2+9x+10}$  

•  $\left(0,0\right)$  

•  $\left(0,\ -\frac{3}{10}\right)$  

•  $\left(0,\ \frac{1}{2}\right)$  
  

• There is no y-intercept.

Unit 4 - Exponential and Logarithmic Functions

Multiple Choice

Examine the function below: 

Which of the following statements about the function is incorrect? 

 $f\left(x\right)=\log_9\left(x-3\right)+1$  

• The graph has a vertical asymptote at x = 3

• The x-intercept is  $\left(\frac{10}{3},\ 0\right)$  

• The point  $\left(12,\ 2\right)$ is on the graph. 

• The y-intercept is  $\left(0,\ \frac{3}{2}\right)$  

Multiple Choice

Which of the following functions has an asymptote at

 $y=-16$  and a y-intercept at  $\left(0,\ -15\right)$  ?

•  $y=4^{x-16}$  

•  $y=4^x-16$  

•  $y=4^{2x}+16$  

•  $y=2\cdot4^x-16$  

Multiple Choice

Simplify this expression $\log_{36}216$  

•  $\frac{3}{2}$  

•  $6$  

•  $\frac{2}{3}$  

•  $\frac{1}{6}$  

Multiple Choice

Given these two statements, which of the following is equal to $x+y$  ?

 $5^x=9$  and    $2^y=5$  

•  $\log_9⁡5+\log_5⁡2$  

•  $\log_5⁡9+\log_2⁡5$  

Open Ended

The population of a community can be represented by the equation below, where p is the population in thousands and t is the number of years since 1990. 


 $p=\log⁡5+\log⁡(t+3)+7$   

Determine the value of t when p = 9.

Multiple Choice

The population of a community can be represented by the equation below, where p is the population in thousands and t is the number of years since 1990. 

 $p=\log⁡5+\log⁡(t+3)+7$  

Which of the following is the correct interpretation of the solution        (17, 9)?

• In 17 years, the population is 9.

• In 9 years, the population is 17.

• In 17 years, the population is 9,000.

• In 9 years the population is 17,000.

Open Ended

Solve the following equation for x.

 $\log_2x+\log_2\left(x-2\right)=3$  

Unit 5 - Trig Functions

Multiple Choice

Which of the following statements is impossible?

• $\sin\theta=\frac{\sqrt{3}}{2}$

• $\sin\theta=1$

• $\sin\theta=\frac{\pi}{10}$

• $\sin\theta=-\pi$

Multiple Choice

Determine the equation of the trigonometric function shown in the graph.

• $y=3\cos\left(2x-\pi\right)+2$

• $y=3\cos\left(x+\frac{\pi}{2}\right)+2$

• $y=-3\cos\left(x-\pi\right)+2$

• $y=3\cos\left(x-\frac{3\pi}{2}\right)+2$