CA Review - 4th 9 Weeks

CA Review - 4th 9 Weeks

Transformations

Multiple Choice

what is the equation that best matches the graph?

• A
• B
• C
• D

Multiple Choice

Referring to f(x) =  $\frac{1}{x}$  which function shifts down 6 units?

• F(x) = $\frac{1}{x-6}$  

• F(x) = $\frac{1}{x}-6$  

• F(x) = $\frac{1}{x+6}$  

• F(x) = $\frac{1}{x}+6$  

Multiple Choice

Referring to f(x)=  $\frac{1}{x}$  how does f(x) =  $\frac{1}{x}+3$  translate?

• Shifts right 3 units.

• Shifts up 3 units.

• Shifts left 3 units.

• Shifts down 3 units.

Multiple Choice

Referring to f(x)=  $\frac{1}{x}$  how does f(x) =  $\frac{1}{x+3}$  translate?. 

• Shifts right 3

• Shifts up three

• Shifts left three

• Shifts down three

Multiple Choice

Which function matches this graph?

• $f\left(x\right)=\frac{1}{x-1}+2$

• $f\left(x\right)=\frac{1}{x+2}-1$

• $f\left(x\right)=\frac{1}{x+1}+2$

• $f\left(x\right)=\frac{1}{x-2}+1$

Multiple Choice

Which is the graph of the rational equation:

Multiple Choice

What is the transformation of the logarithmic function
 $f\left(x\right)=\log\ \left(x+3\right)-1$  

• left 3, right 1

• right 3, down 1

• right 3, up 1

• left 3, down 1

Multiple Choice

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

• g(x)=log₃(x+6)+4

• g(x)=log₃(x+4)-6

• g(x)=log₃(x-6)+4

• g(x)=3log(x+6)+4

Multiple Choice

Write the equation of the function f(x)=log(x+5)-6 after the following transformations:

Translate 3 units left and 2 units up.

• f(x)=log(x+2)+2

• f(x)=log(x+2)-4

• f(x)=log(x+8)-4

• f(x)=log(x+8)+2

Convert exponential to logarithmic and back

b^x=a --> log_b(a)=x

Multiple Choice

Convert Log₃(x) = 4 to an exponent

• 3^x = 4

• 3⁴ = x

• x³ = 4

• 4^x = 3

Multiple Choice

Convert Log₂(64) = y to an exponent

• 64^y = 2

• 2⁶⁴ = y

• 64² = y

• 2^y = 64

Multiple Choice

Convert 4^x = 64 to a Log

• Log₆₄(x) = 4

• Log_x(64) = 4

• Log₄(64) = x

• Log₄(x) = 64

Multiple Choice

Convert 16 = 2^x to a Log

• Log₂(x) = 16

• Log₂(16) = x

• Log₁₆(x) = 2

• Log_x(16) = 2

Asymptotes and Domain

Multiple Choice

Find the domain of the function.  $f(x)=\frac{x}{2x+4}$  

• x cannot equal to 2

• x cannot equal to 1/2

• x cannot equal to -2

• All real numbers

Multiple Choice

Find the domain of the function.  $f(x)=\frac{x^3}{x+8}$  

• x cannot equal to 8

• x cannot equal to 0

• x cannot equal to -8

• All real numbers

Multiple Select

 $h\left(x\right)=\frac{x\left(x-3\right)\left(x-6\right)\left(x+5\right)}{3x\left(x+3\right)\left(x-6\right)\left(x+7\right)}$  

Identify the vertical asymptote(s).

**Select all that apply**

• x=0

• x=-3

• x=6

• x=-7

• x=3

Multiple Choice

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$   

• No vertical asymptotes.

• One vertical asymptote: x = 4

• Two vertical asymptotes: x = -3 and x = -7

• Three vertical asymptotes:  x = -3, x = 4, and x = -7

Multiple Choice

What is/are the Vertical Asymptote(s)?

• x= -4

• x= -4, x= 5

• x= -5, x= 5

• x= 4

Multiple Choice

What is the Vertical Asymptotes? 

• x= -5
• x= 5
• x= 6
• x= -6

Multiple Choice

What is the horizontal asymptote?

• y = -4
• y = 1
• x = 1
• y = -6

Multiple Choice

What is/are the vertical asymptote(s)?

• x=-2
• x=2 and x=3
• x=-3
• x=3

Multiple Choice

What is the horizontal asymptote to this function?

• y=4
• y=0
• y=-2
• y=1

Multiple Choice

What is the asymptote for the logarithmic function

 $f\left(x\right)=\log\left(x-1\right)$  

• x=1

• x=-1

• y=1

• y=-1

Multiple Choice

What kind of asymptotes do logs have?

• horizontal ( y=0)
• vertical (x=0)

Multiple Choice

find the asymptote: y = log₁₀ (x+3)

• x=-3
• x=3
• y=-3
• y=3

Multiple Choice

What is the slant (Oblique) asymptote for the equation

f(x) = (x² - 4x + 2)/(x + 3)

• y = x -1

• y = x -7

• y = -7x + 23

• y = -2x + 2

Multiple Choice

Find the oblique asymptote.

• y = 3x - 12
• y = x + 5
• y = 3x - 5
• y = 3x - 7

Solve Exponential Equations

Multiple Choice

You invest an initial amount of $300 into an account at an interest rate of 14%. The equation y=300(1.14)^t can be used to determine the amount in the account each year. How long will it take for there to be $7200 in the account?

• 24.3 years

• 4 years

• 21 years

• 26 years

Multiple Choice

Solve the following equation for t. $y=P\cdot4^{-\frac{t}{33}}$  

•  $t=-33\ \log_4\ \frac{y}{P}$  

•  $t=33\ \log_4\ \frac{y}{P}$  

•  $t=\frac{\log_4\ \frac{y}{P}}{-33}$  

•  $t=\frac{\log_4\ \frac{y}{P}}{33}$  

Inverse Variation

Multiple Choice

The cost per person to rent a mountain cabin is inversely proportional (varies inversely) to the number of people who share the rent. If the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?

• $22.50
• $57.60
• $1.11
• $12.50

Multiple Choice

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

• 14
• 10
• 2
• -14

Operations with Rational Expressions

Multiple Choice

 $\frac{10m-20}{10m+70}\times\frac{m^2+8m+7}{m+1}$  

•  $\frac{m+2}{3}$  

•  $\frac{3}{20}$  

•  $m-2$  

•  $\frac{m+4}{m+7}$  

Multiple Choice

Multiply and Simplify

 $\left(x+2\right)\cdot\frac{x+5}{x^2-4}$  

•  $\frac{\left(x+5\right)}{x+4}$  

•  $\frac{x-2}{x+5}$  

•  $\frac{x+5}{\left(x+4\right)}$  

•  $\frac{x+5}{x-2}$  

Multiple Choice

Divide the Rational Expression
 $\frac{x^2-4x-5}{x^2-3x+2}\div\frac{x^2-3x-10}{x^2-4}$  

•  $\frac{x-5}{x-1}$  

•  $\frac{x+1}{x-1}$  

•  $\frac{1}{x-1}$  

•  $x+1$  

Multiple Choice

 $\frac{b-4}{b^2-14b+40}\div\frac{b^2+6b+8}{b^2-3b-70}$  

•  $\frac{b-3}{6}$  

•  $\frac{2b}{9}$  

•  $\frac{5b\left(b-6\right)}{7}$  

•  $\frac{b+7}{\left(b+4\right)\left(b+2\right)}$  

Multiple Choice

Multiply and simplify.
 $\frac{3x-27}{x^2-36}\cdot\frac{x^2-x-30}{x-9}$  

•  $\frac{3\left(x+5\right)}{x+6}$  

•  $\frac{x+5}{x+6}$  

•  $\frac{3}{\left(x+6\right)\left(x+5\right)}$  

Multiple Choice

Solve by cross-multiplying.

• x = -1, 5
• No Solution
• x = -4, 5
• x= -4

Multiple Choice

Solve for x

• 11
• 5
• 8
• 7

Multiple Choice

Solve and check for extraneous solutions

• k = 20

• k = -20

• No Solution

• k = 3

Multiple Choice

Solve the equation for x.

• 6
• 12
• 0
• 3