Identifying Key Features of Functions (Grades 11-12)

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Identifying Key Features of Functions

1. 
Given the graph below of the function [math]f(x) = 2^x[/math], what is the end behavior as [math]x -> -oo ?[/math] Assume 1 unit intervals for both axes.
Graph - Exponent Function y=2^x
  1. [math]f(x) -> -oo[/math]
  2. [math]f(x) -> 0[/math]
  3. [math]f(x) -> -1[/math]
  4. [math]f(x) -> oo[/math]
2. 
Given the graph of the function [math]f(x) = log(x)[/math], for what values of x is the function positive? Assume 1 unit intervals for both axes.
Graph - Log Function y=log x
  1. [math]-oo < x < oo[/math]
  2. [math] 0 < x < 1[/math]
  3. [math]x>1[/math]
  4. [math]x > 0[/math]
3. 
For the absolute value function shown below, where is the function decreasing? Assume 1 unit intervals for both axes.
Graph - Absolute Function y=|1/2x|
  1. The function is never decreasing.
  2. For all values of x.
  3. [math]x>0[/math]
  4. [math]x<0[/math]
4. 
The following table lists some values for a function, [math]f(x)[/math]. What conclusion can be reached about this function from these function values?

[math] \ \ \ \ \mathbf{x} \ \ \ \ [/math][math] \ \ \ \ \mathbf{f(x)} \ \ \ \ [/math]
[math] -1.5 [/math][math] 1.38 [/math]
[math] -1.25 [/math][math] 2.64 [/math]
[math] -1[/math][math] 3 [/math]
[math] -0.75[/math][math] 2.73 [/math]
[math] -.5[/math][math] 2.13 [/math]
  1. The function is positive for [math]-oo < x < 0[/math].
  2. The function is increasing for [math]-oo < x < -1[/math].
  3. The function is positive for all values of x.
  4. The function has a relative maximum near [math]x=-1[/math].
5. 
Given the table for certain values of a function, [math]f(x)[/math], which of the following is most likely a feature of this function?

[math] \ \ \ \ \mathbf{x} \ \ \ \ [/math][math] \ \ \ \ \mathbf{f(x)} \ \ \ \ [/math]
[math] -3 [/math][math] -27 [/math]
[math] -2 [/math][math] -8 [/math]
[math] -1[/math][math] -1 [/math]
[math] 0[/math][math] 0 [/math]
[math] 1[/math][math] 1 [/math]
[math] 2[/math][math] 8 [/math]
[math] 3[/math][math] 27 [/math]
  1. It has odd symmetry.
  2. It is decreasing on [math]-oo < x < 0[/math].
  3. The value of the function approaches 0 as [math]x-> oo[/math].
  4. There is a relative minimum at [math]x= -3[/math].
6. 
The table below gives some of the values of a function, [math]f(x)[/math]. Which of the following is most likely true, using only the data from the table?

[math] \ \ \ \ \mathbf{x} \ \ \ \ [/math][math] \ \ \ \ \mathbf{f(x)} \ \ \ \ [/math]
[math] -0.5 [/math][math] 1.03 [/math]
[math] 0 [/math][math] 2 [/math]
[math] 0.5[/math][math] 1.03 [/math]
[math] 1[/math][math] -1.5 [/math]
[math] 1.5[/math][math] -4.47 [/math]
[math] 2[/math][math] -7 [/math]
[math] 2.5[/math][math] -3.47 [/math]
  1. The function is negative on the interval [math](0,2)[/math]
  2. The function is decreasing on the interval [math](0,oo)[/math].
  3. The function is decreasing on the interval [math](0,2)[/math]
  4. The function is positive on the interval [math](-oo,0)[/math].
7. 
Given the function [math]f(x) = x^2 - 2x - 3[/math], for what interval(s) is [math]f(x) > 0 ?[/math]
  1. [math](-1,3)[/math]
  2. [math](-oo,-1) uu (3,oo)[/math]
  3. [math](-oo , 0)[/math]
  4. [math](-oo, oo)[/math]
8. 
For the function [math]f(x) = -x^2 - 4[/math], for what interval(s) is [math]f(x) < 0 ?[/math]
  1. [math](-oo,-2) uu (2,oo)[/math]
  2. [math](-2,2)[/math]
  3. [math] (-oo,oo)[/math]
  4. [math](0,oo)[/math]
9. 
At what interval is slope of the function [math]y=(x+2)^2[/math] positive?
  1. [math]x<0[/math]
  2. [math]x>0[/math]
  3. [math]x> -2[/math]
  4. [math]x<2[/math]
10. 
At what interval is slope of the function [math]y=-(x-2)^2[/math] positive?
  1. [math]x<0[/math]
  2. [math]x>0[/math]
  3. [math]x> -2[/math]
  4. [math]x<2[/math]

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