2. Graphs of Equations

Graphs and Coordinates

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## Graphs & the Rectangular Coordinate System

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## Graphs and Coordinates - Example

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PRACTICE PROBLEMS AND ACTIVITIES (33)

- Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = x^2-3
- In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 2, 3)
- In Exercises 6–8, use the graph and determine the x-intercepts if any, and the y-intercepts if any. For each g...
- Fill in the blank(s) to correctly complete each sentence. The function g(x)=√x has domain ________.
- In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 4, 0)
- In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 5/2, 3/2)
- Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = x^2 - 2
- Determine the intervals of the domain over which each function is continuous. See Example 1.
- Use the vertical line test to identify graphs in which y is a function of x.
- Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = x + 2
- Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = - (1/2)x + 2
- In Exercises 11–26, determine whether each equation defines y as a function of x. y = - √x +4
- Determine whether the three points are the vertices of a right triangle. See Example 3. (-6,-4),(0,-2),(-10,8)
- Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = 9 - x^2
- In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.f(x)=4...
- Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = x^3 - 1
- In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.g(x) =...
- In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if ...
- Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=√(4x...
- In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if ...
- In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select inte...
- In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation. The...
- In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation. y =...
- Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(0)
- Graph each function. Give the domain and range. See Example 3. ƒ(x)=[[2x]]
- In Exercises 55–64, use the vertical line test to identify graphs in which y is a function of x.
- Determine whether each function is even, odd, or neither. See Example 5. ƒ(x)=x^3-x+9
- Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(3t-2)
- Use the graph of g to solve Exercises 71–76. Find g(-4)
- Graph each function. ƒ(x) = -√x - 2
- In Exercises 75–78, list the quadrant or quadrants satisfying each condition. x^3 > 0 and y^3 <0
- In Exercises 77–92, use the graph to determine a. the function's domain; b.the x-intercepts, if any; and e. th...
- In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-int...