Comparing Different Function Representations (Grade 10)

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Comparing Different Function Representations

1. 
At what values of the domain is the function [math]f(x)= x+2[/math] greater than the function represented in the graph below?
Graph - Quadratic Function y=-x^2
  1. All real numbers
  2. Nowhere
  3. [math]0 < x <2[/math]
  4. [math]-2 < x < 2[/math]
2. 
At what values of the domain is the function [math]f(x)= x-2[/math] less than the function represented in the graph?
Graph - Quadratic Function y=-x^2
  1. All real numbers
  2. Nowhere
  3. [math]-1 < x < 0[/math]
  4. [math]-2 < x < 1[/math]
3. 
At what values of the domain is the function [math]f(x)= x-2[/math] less than the function represented in the graph?
Graph - Linear Function y=2x ?
  1. All real numbers
  2. [math]x > 0[/math]
  3. [math]-1 < x < 0[/math]
  4. [math]-2 < x [/math]
4. 
For what values of the domain is the function [math]f(x)= 2x-2[/math] less than the function represented in the graph?
Graph - Linear Function y=2x
  1. All real numbers
  2. [math]x > 0[/math]
  3. [math]-1 < x < 0[/math]
  4. [math]-2 < x [/math]
5. 
For what values of [math]x[/math] is the function [math]f(x)= 2x^2+2[/math] greater than the function presented in the graph?
Graph - Quadratic Function y=1/2x^2
  1. All real numbers
  2. [math]x = 0[/math]
  3. [math]-1 < x < 1[/math]
  4. Never
6. 
For what values of [math]x[/math] is the function [math]g(x) = -1/2 x^2 + x + 2[/math] greater than the function shown in the graph below?
Graph - Quadratic Function y=1/2x^2
  1. For all values of x.
  2. For [math]-1 < x <2[/math].
  3. For [math]-2 < x < 1[/math].
  4. The function [math]g(x)[/math] is never greater than the function shown in the graph.
7. 
Given two linear functions, [math]f(x)[/math] which has some of its values listed in the table and [math]g(x)[/math] represented graphically, determine which function has a greater slope. If the slopes are equal, determine whether the lines are coincident or not. Let [math]m_f[/math] represent the slope of function [math]f[/math] and [math]m_g[/math] represent the slope of function [math]g[/math].

[math] \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ [/math]
[math] -2 [/math][math] 7 [/math]
[math] -1 [/math][math] 4 [/math]
[math] 0 [/math][math] 1 [/math]
[math] 1 [/math][math] -2 [/math]
[math] 2 [/math][math] -5 [/math]


Graph - Linear Function y=2x
  1. [math]m_f > m_g[/math]
  2. [math]m_f < m_g[/math]
  3. [math]m_f = m_g[/math] The lines are not coincident.
  4. [math]m_f = m_g[/math] The lines are coincident.
8. 
If [math]g(x)[/math] is a linear function, some of whose values are listed in the table below, and [math]f(x) = 3x-2[/math], which of the following is/are true? There may be more than one correct answer.

[math] \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \mathbf{g(x)} \ \ \ \ \ \ \ \ \ [/math]
[math] -2 [/math][math] -3 [/math]
[math] -1 [/math][math] -5/2 [/math]
[math] 0 [/math][math] -2 [/math]
[math] 1 [/math][math] -3/2 [/math]
[math] 2 [/math][math] -1 [/math]
[math] 3 [/math][math] -1/2 [/math]
[math] 4 [/math][math] 0 [/math]
[math] 5 [/math][math] 1/2 [/math]
  1. Both functions have the same slope.
  2. Both functions have a y-intercept of -2.
  3. Both functions have an x-intercept of 2/3.
  4. If graphed, both functions would have values in quadrants I, III, and IV.
9. 
A company sells coffee mugs. Its cost function is [math]C(x) = 1/2 x + 200[/math], where [math]x[/math] is the number of coffee mugs sold, and [math]C[/math] is the cost to produce them, in dollars. The table below shows the revenue given the number of coffee mugs sold. With the given data, how many coffee mugs should the company sell in order to make a profit?

[math] \ \ \ \ \ \ \ \ \ mathbf{"Coffee Mugs Sold"} \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \mathbf{"Revenue"} \ \ \ \ \ \ \ \ \ [/math]
[math] 0 [/math][math] $0 [/math]
[math] 100 [/math][math] $206.00 [/math]
[math] 200 [/math][math] $374.00 [/math]
[math] 300 [/math][math] $504.00 [/math]
[math] 400 [/math][math] $596.00 [/math]
[math] 500 [/math][math] $650.00 [/math]
[math] 600 [/math][math] $665.00 [/math]
[math] 700 [/math][math] $644.00 [/math]
[math] 800 [/math][math] $584.00 [/math]
  1. More than zero coffee mugs.
  2. Between 400 and 700 coffee mugs.
  3. Between 200 and 700 coffee mugs.
  4. 600 coffee mugs.
10. 
Shawn's class has been learning about rockets and is planning to launch a small model rocket of their own. The rocket will be launched from ground level, straight up into the air. The rocket does not have a parachute. The class has determined the theoretical height and time of the rocket's flight, as modeled by the following function.

[math]f(t) = -5t^2 + 100t[/math]

For this function, f(t) is the height of the rocket in meters, and t is the duration of the flight in seconds. When they actually fire the rocket, it lands 18 seconds after it was fired. Shawn was on top of a nearby structure that is 35 meters high. He measured that the rocket, as it ascended, passed him 0.5 seconds after it launched.

Was the theoretical calculation correct, in terms of the maximum height of the rocket? If not, by how much did it over- or underestimate the rocket's maximum height?
  1. The theoretical calculation was correct, the rocket reached a maximum height of 500 m.
  2. The theoretical calculation underestimated the height by 140 m.
  3. The theoretical calculation overestimated the height by 419 m.
  4. The theoretical calculation overestimated the height by 176 m.

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