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Practice Problems in Graphing and Linear Equations, Exams of Algebra

University of Illinois - ChicagoAlgebra

Practice problems for graphing ordered pairs, functions, and linear equations. It includes instructions for plotting points, graphing functions, finding intercepts, and determining slopes. The document also covers graphing inequalities and finding their intersections.

Typology: Exams

Pre 2010

Uploaded on 07/29/2009

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koofers-user-df4 ๐Ÿ‡บ๐Ÿ‡ธ

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practice problems
D. Benjamin Antieau
26 June 2008
Plot the following ordered pairs: {(โˆ’4,5),(3,2),(โˆ’5,0),(2,5),(1,4.5),(1.5,2)}.
Graph the following functions.
1. xโˆ’y= 2.
2. 3x+ 5y= 10.
3. x+y= 0.
4. 7x+y= 2.
5. 13x+ 13y= 1.
Grapth the following functions by finding the values at x=โˆ’2,โˆ’1,0,1,2.
1. f(x) = x2+ 2xโˆ’3.
2. f(x) = |2x|+ 1.
3. f(x) = x3.
Graph the following linear equations. Then, find the xand y-intercepts.
Then, find the slopes.
1. f(x) = โˆ’x+ 5.
2. f(x) = 2xโˆ’3.
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practice problems

D. Benjamin Antieau

26 June 2008

Plot the following ordered pairs: {(โˆ’ 4 , 5), (3, 2), (โˆ’ 5 , 0), (2, 5), (1, 4 .5), (1. 5 , 2)}.

Graph the following functions.

  1. x โˆ’ y = 2.
  2. 3x + 5y = 10.
  3. x + y = 0.
  4. 7x + y = 2.
  5. 13x + 13y = 1.

Grapth the following functions by finding the values at x = โˆ’ 2 , โˆ’ 1 , 0 , 1 , 2.

  1. f (x) = x^2 + 2x โˆ’ 3.
  2. f (x) = | 2 x| + 1.
  3. f (x) = x^3.

Graph the following linear equations. Then, find the x and y-intercepts. Then, find the slopes.

  1. f (x) = โˆ’x + 5.
  2. f (x) = 2x โˆ’ 3. 1
  1. f (x) = 12 x + 4.

Find the slopes of the lines through each of the following pairs of points.

  1. {(โˆ’ 5 , 5), (0, 0)}.
  2. {(โˆ’ 2 , 3), (3, 3)}.
  3. {(4, 2), (โˆ’ 1 , โˆ’1)}.

What are the slopes of the following lines?

  1. f (x) = โˆ’ 271 x + 9.
  2. g(x) = 1000x + 1000000.
  3. h(x) = 32.

Draw a line with the given slope through the given point.

  1. slope: -1, point: (0,4).
  2. slope: 3, point: (1,1).
  3. slope: 5, point: (1,0). Note that in the first example the given point is the y-intercept, and that in the third it is the x-intercept.

Graph each of the following inequalities by first graphing the boundary line, and then choosing a test point off of the boundary line to determine which area to fill in.

  1. x < 4.
  2. x โ‰ฅ โˆ’3.
  3. 4x + 4y > 2.

Now, graph the intersection of the following two inequalities. x > 2 and 3 x + y โ‰ค 4.

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