2. Graphs of Equations

Two-Variable Equations

2. Graphs of Equations

# Two-Variable Equations - Video Tutorials & Practice Problems

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## Equations with Two Variables

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## Graphing Equations of Two Variables by Plotting Points

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ProblemGraph the equation $y-x^2+3=0$ by choosing points that satisfy the equation**.**

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ProblemGraph the equation $y=\sqrt{x}+1$ by choosing points that satisfy the equation**.** (*Hint: Choose positive numbers only*)

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## Graphing Intercepts

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PRACTICE PROBLEMS AND ACTIVITIES (35)

- In Exercises 1-12, plot the given point in a rectangular coordinate system. (1, 4)
- Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = 2x-2
- Determine whether each equation defines y as a function of x. 2x + y = 8
- Fill in the blank to correctly complete each sentence. The x-intercept of the graph of 2x + 5y = 10 is _______...
- In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 16
- In Exercises 1-12, plot the given point in a rectangular coordinate system. (7/2, - 3/2)
- Determine whether each relation defines a function. See Example 1. {(-3,1),(4,1),(-2,7)}
- Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = x - 2
- For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3).See Example 2. ƒ(x)={2+...
- For each graph, determine whether y is a function of x. Give the domain and range of each relation.
- Graph each piecewise-defined function. See Example 2. ƒ(x)={6-x if x≤3, 3 if x>3
- Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.
- Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = |x| + 1
- Determine whether each equation defines y as a function of x. y = 6 -x^2
- In Exercises 11–26, determine whether each equation defines y as a function of x. |x|- y = 5
- Determine whether the three points are the vertices of a right triangle. See Example 3. (-4,3),(2,5),(-1,-6)
- In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) ...
- In Exercises 31–32, the domain of each piecewise function is (-∞, ∞) (a) Graph each function. (b) Use the gra...
- In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) ...
- In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) ...
- Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Exam...
- In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if ...
- For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the eq...
- In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation. The...
- Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[x]], for x=x-(-π)
- Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(1/3)
- In Exercises 55–64, use the vertical line test to identify graphs in which y is a function of x.
- Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(-x)
- In Exercises 55–64, use the vertical line test to identify graphs in which y is a function of x.
- In Exercises 71–74, determine whether each statement is true or false. If the statement is false, make the nec...
- In Exercises 77–92, use the graph to determine a.the x-intercepts, if any; b. the y-intercept, if any; and e. ...
- In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-int...
- Determine the largest open intervals of the domain over which each function is b) decreasing. See Example 9.
- Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the orig...
- In Exercises 95–96, let f and g be defined by the following table: Find √(ƒ(−1) − f(0)) – [g (2)]² + ƒ(−2) ÷ g...