Advanced Pre-Calculus Practice: Section 1-3

Between which consecutive integers are the real zeros of the function

f(x) = x³ +2x²-5x+1

on the interval [-1, 3]? Select all that apply.

• [-1, 0]

• [0, 1]

• [1, 2]

• [2, 3]

Is the function $\frac{x^2-36}{x+2}$  continuous at x = 3?  If discontinuous, identify the type of discontinuity.

• continuous

• jump discontinuity

• infinite discontinuity

• removable discontinuity

Is the function $\frac{x^2-36}{x+2}$  continuous at x = -2?  If discontinuous, identify the type of discontinuity.

• continuous

• jump discontinuity

• infinite discontinuity

• removable discontinuity

What is the end behavior of the function

 $f\left(x\right)\ =\ \frac{1}{x^2-3}-5$  ?

• As $x\rightarrow\infty$  ,  $f\left(x\right)\rightarrow5$  and as  $x\rightarrow-\infty$  ,  $f\left(x\right)\rightarrow\infty$  

• As $x\rightarrow\infty$  ,  $f\left(x\right)\rightarrow\infty$  and as  $x\rightarrow-\infty$  ,  $f\left(x\right)\rightarrow\infty$  

• As $x\rightarrow\infty$  ,  $f\left(x\right)\rightarrow-5$  and as  $x\rightarrow-\infty$  ,  $f\left(x\right)\rightarrow-5$  

• As $x\rightarrow\infty$  ,  $f\left(x\right)\rightarrow\infty$  and as  $x\rightarrow-\infty$  ,  $f\left(x\right)\rightarrow-\infty$  

Is the function

 $\frac{x^2-81}{x+9}$  

continuous at x = 9?  If discontinuous, identify the type of discontinuity.

• continuous

• jump discontinuity

• infinite discontinuity

• removable discontinuity

Is the function

 $\frac{x^2-81}{x+9}$  

continuous at x = -9?  If discontinuous, identify the type of discontinuity.

• continuous

• jump discontinuity

• infinite discontinuity

• removable discontinuity

What is the end behavior of the function

 $f\left(x\right)\ =\ -x^3+4x^2-x+3$  ?

• As $x\rightarrow\infty$  ,  $f\left(x\right)\rightarrow-\infty$  and as  $x\rightarrow-\infty$  ,  $f\left(x\right)\rightarrow\infty$  

• As $x\rightarrow\infty$  ,  $f\left(x\right)\rightarrow\infty$  and as  $x\rightarrow-\infty$  ,  $f\left(x\right)\rightarrow\infty$  

• As $x\rightarrow\infty$  ,  $f\left(x\right)\rightarrow-\infty$  and as  $x\rightarrow-\infty$  ,  $f\left(x\right)\rightarrow-3$  

• As $x\rightarrow\infty$  ,  $f\left(x\right)\rightarrow3$  and as  $x\rightarrow-\infty$  ,  $f\left(x\right)\rightarrow3$  

Between which consecutive integers are the real zeros of the function

f(x) = x³ +3x²--1

on the interval [-4, 0]? Select all that apply.

• [-4, -3]

• [-3, -2]

• [-2, -1]

• [-1, 0]

Is f(x) continuous at x = -2?  If discontinuous, identify the type of discontinuity.

• continuous

• jump discontinuity

• infinite discontinuity

• removable discontinuity

Is f(x) continuous at x = 4?  If discontinuous, identify the type of discontinuity.

• continuous

• jump discontinuity

• infinite discontinuity

• removable discontinuity