Algebra II - Unit 2 - Non-Linear Functions Review

The graph below is an example of which type of function?

• quadratic

• linear

• cubic

• square root

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach negative infinity. To which family of functions might the described function belong?

• absolute value

• exponential

• cube root

• square root

The graph of y =  $\sqrt{x}$  is transformed as shown in the graph below. Which equation represents the transformed function? 

•  $y\ =\ -\sqrt{x}+\ 2$  

•  $y\ =\ \sqrt{\left(-x\right)}+\ 2$  

•  $y\ =\ \sqrt{\left(-x\right)}-\ 2$  

•  $y\ =\ -\ \sqrt{x}-\ 2$  

How is the graph of  $y\ =\ -^3\sqrt{x\ -\ 4}$  transformed to produce the graph of  $y\ =\ -^3\sqrt{2x}-\ 4$ ?

• The graph is stretched horizontally by a factor of 2 and then moved right 4 units.

• The graph is compressed horizontally by a factor of 2 and then moved down 4 units.

• The graph is compressed horizontally by a factor of 2, moved left 4 units, and then moved down 4 units.

• The graph is stretched horizontally by a factor of 2, moved left 4 units,  and then moved down 4 units.

Which statement best compares the graphs of  $f\left(x\right)\ =\ \lfloor x\rfloor\ and\ f\left(x\right)\ =\ \lceil x\rceil?$  

• The two graphs are exactly the same.

• The open and closed circles are reversed.

• The graph of f(x) =  $\lceil x\rceil$  is shifted up compared to the graph of f(x) =  $\lfloor x\rfloor$ , and the open and closed circles are reversed.

• The graph of f(x) =  $\lceil x\rceil$  is shifted up compared to the graph of f(x) =  $\lfloor x\rfloor$ , and the open and closed circles are the same.

Which of the following describes the graph of  $y\ =\ \lfloor x\ -\ 2\rfloor?$ 

• The graph has closed circles on the left of each step and open circles on the right and includes the step y = -4 for  $-2\le x<-1.$  

• The graph has closed circles on the left of each step and open circles on the right and includes the step y = -3 for  $-2<x\le-1.$  

• The graph has open circles on the left of each step and closed circles on the right and includes the step y = -4 for  $-2\le x<-1.$  

• The graph has open circles on the left of each step and closed circles on the right and includes the step y = -3 for  $-2\le x<-1.$  

An international calling plan charges 45 cents per minute or fraction of a minute for each call. Which graph models the cost, y, in cents of making x minutes of international calls?

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The equation of the piecewise function f(x) is above. What is the value of f(–2)?

• f(-2) = -6

• f(-2) = -4

• f(-2) = 0

• f(-2) = 3

What is the range of the function graphed above?

• $\left(-\infty,\ 4\right]$

• $\left[-4,\ 0\right)\ U\ \left[2,\ \infty\right)$

• $\left[-4,\ \infty\right)$

• $\left(-4,\ 0\right]\ U\ \left(2,\ \infty\right)$

Which of the following accurately lists all discontinuities of the function above?

• point discontinuity at x = -2.

• point discontinuity at x = 4; jump discontinuity at x = -2.

• point discontinuities at x = -4 and x = 4; jump discontinuity at x = -2.

• jump discontinuities at x = -4, x = -2, and x = 4.