Quiz 4-5 Review over asymptotes

Quiz 4-5 Review over asymptotes

Factor

Multiple Choice

Factor
x² + 9x - 36

• (x + 12)(x - 3)
• (x + 9)(x - 4)
• (x - 12)(x + 3)
• (x - 9)(x - 4)

Multiple Choice

Factor
a² - a - 12

• (a - 4)(a + 3)
• (a + 6)(a - 4)
• (a - 6)(a + 4)
• (a + 4)(a - 3)

Multiple Choice

Factor

x² - 9x - 36

• (x + 12)(x - 3)

• (x + 9)(x - 4)

• (x - 12)(x + 3)

• (x - 9)(x - 4)

Multiple Choice

Factor:
x² + 7x - 30

• (x + 10)(x - 7)
• (x - 10)(x + 3)
• (x + 10)(x + 3)
• (x + 10)(x - 3)

Vertical Asymptotes

How to find the vertical asymptote when given only a function?

• set the denominator equal to 0

• solve for x

Multiple Select

Find the vertical asymptote of the following function: $f\left(x\right)=\frac{x-1}{x^2-2x-15}$  

• x=-3

• x=3

• x=-5

• x=5

• x=2

Horizontal Asymptotes

Rules

• N<D : y = 0

• N>D: no Horizontal Asymptote

• N=D: y=a/b (divide the leading coefficients)

Multiple Choice

What is the horizontal asymptote of the following function? $f\left(x\right)=\frac{7x^2-5}{x+1}$  

• x = 7

• y = 7

• x = 0

• y = 0

• No HA

Multiple Choice

What is the horizontal asymptote of the following function? $f\left(x\right)=\frac{7x^2-5}{x^2+1}$  

• x = 7

• y = 7

• x = 0

• y = 0

• No HA

Multiple Choice

What is the horizontal asymptote of the following function? $f\left(x\right)=\frac{7x^{ }-5}{x^2+1}$  

• x = 7

• y = 7

• x = 0

• y = 0

• No HA

Slant Asymptotes

Only find if there is No Horizontal Asymptote. Use long division!

Multiple Choice

What is the slant asymptote of the following function? $f\left(x\right)=\frac{x^2+x-5}{x+4}$  

• y=x+5

• y=x+4

• y=x-3

• y=-3x-5

• y=0

Graph match

Multiple Choice

Which graph matches the equation $f\left(x\right)=\frac{x^2\ }{x-2}$  

Multiple Choice

Which graph matches the equation $f\left(x\right)=\frac{x^2\ }{x+2}$  

Multiple Choice

Which graph matches the equation $f\left(x\right)=\frac{x-1}{x^2-3x-10}$  

Multiple Choice

Which graph matches the equation $f\left(x\right)=\frac{x-1}{x^2+3x-10}$  

Multiple Choice

Which graph matches the equation $f\left(x\right)=\frac{5\ }{x+3}$  

Multiple Choice

Which graph matches the equation $f\left(x\right)=\frac{5\ }{x-3}$