Functions: Graphs, Tables, & Equations (Grade 10)

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Functions: Graphs, Tables, & Equations

1. 
The relation graphed below is a function.
Graph - Piecewise Random 1
  1. True
  2. False
2. 
The graph below shows a function.
Graph - Quadratic Function y=-1/2x^2
  1. True
  2. False
3. 
Is the following a function? Explain why or why not.
Coordinate Plane - 5x5 - With Dots
  1. Yes, this does represent a function, because all the points are distinct (none of them are coincident).
  2. No, this does not represent a function, since a function can not be made up of only points.
  3. No, this does not represent a function, since it fails the vertical line test.
  4. No, this does not represent a function, since a function is made up of many more points.
4. 
Choose the correct missing entry in the table for the function graphed below. Assume 1 unit intervals for both axes.

[math] \ \ \ \ \mathbf{x} \ \ \ \ [/math][math] \ \ \ \ \mathbf{f(x)} \ \ \ \ [/math]
[math] -2 [/math][math] 2 [/math]
[math] -1 [/math][math] [/math]
[math] 0[/math][math] 0 [/math]
[math] 1[/math][math] 1 [/math]
[math] 2[/math][math] 2 [/math]

Graph - Absolute Function y=|x|
  1. [math]1/2[/math]
  2. [math]-1[/math]
  3. [math]1[/math]
  4. This is not a function.
5. 
Using the function graphed below (assuming the horizontal axis represents x and the vertical axis represents y), fill in the missing value in the corresponding table. Assume the horizontal axis represents x, and the vertical axis represents f(x).


[math] \ \ \ \ \mathbf{x} \ \ \ \ [/math][math] \ \ \ \ \mathbf{f(x)} \ \ \ \ [/math]
[math] -2 [/math][math] -4 [/math]
[math] -1 [/math][math] -2 [/math]
[math] 0[/math][math] 0 [/math]
[math] 1[/math][math] 2 [/math]
[math] 2[/math][math] [/math]

Graph - Linear Function y=2x
  1. 2
  2. 3
  3. 4
  4. 5
6. 
For the function graphed below, where is its output greater than 1? Assume 1 unit intervals for both axes.
Graph - Exponent Function y=2^x
  1. [math]x>0[/math]
  2. [math]-oo < x < oo[/math]
  3. [math]y>0[/math]
  4. [math]y>2[/math]
7. 
Where is the output of the function graphed below less than 2? Assume the horizontal axis represents [math]x[/math] and the vertical axis represents [math]y[/math].
Graph - Quadratic Function y=1/2x^2
  1. [math]x<2[/math]
  2. [math]-2 < y < 2[/math]
  3. [math]-2 < x < 2[/math]
  4. [math]y<2[/math]
8. 
Given the table below, which of the following function rules defines this relationship?

[math] \ \ \ \ \mathbf{x} \ \ \ \ [/math][math] \ \ \ \ \mathbf{f(x)} \ \ \ \ [/math]
[math] -2[/math][math]23 [/math]
[math] -1[/math][math]2 [/math]
[math] 0[/math][math]-1 [/math]
[math] 1[/math][math]-4 [/math]
[math] 2[/math][math]-25 [/math]
  1. [math]f(x) = -8x + 5 [/math]
  2. [math]f(x) = -3x^3 -1 [/math]
  3. [math]f(x) = -3x^2 - 2 [/math]
  4. [math]f(x) = -2x^4 - 8[/math]
9. 
Given the table below (where output values are rounded to one decimal place), which of the following function rules defines this relationship?


[math] \ \ \ \ \mathbf{x} \ \ \ \ [/math][math] \ \ \ \ \mathbf{f(x)} \ \ \ \ [/math]
[math] -2[/math][math]-2.6 [/math]
[math] -1[/math][math]-1.2 [/math]
[math] 0[/math][math]0 [/math]
[math] 1[/math][math]-1.2 [/math]
[math] 2[/math][math]-2.6 [/math]
  1. [math]f(x) = -|1.4x|[/math]
  2. [math]f(x) = -|1.2x| [/math]
  3. [math]f(x) = 1.3x [/math]
  4. [math]f(x) = 3e^(-0.5x^2)-3 [/math]
10. 
Given two polygons, the first one having more sides than the second, let the following rule describe how to map the first polygon to the second polygon. (To help illustrate, refer to the two polygons pictured below.) Label the vertices of each polygon A, B, C, etc. Then, each vertex of polygon 1 is mapped to its corresponding vertex on polygon 2 (A to A, B to B, etc.). For all extra vertices of the first polygon (in this case G and H), they map to the final vertex of the second polygon (in this case to F). Is this rule a function? If not, why not?

Polygon 1: Octagon ABCDEFGH
Polygon 2: Hexagon ABCDEF
  1. Yes, this is a function.
  2. No, functions relate only to equations and graphs.
  3. No, because multiple vertices of the first polygon are mapped to the same vertex on the second polygon, which is the same as failing the vertical line test.
  4. No, because this is not continuous; there is only a finite set of points, while functions (graphs) are an infinite set of points.

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