2. Graphs of Equations

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+x if x<-4, -x if -4≤x≤2, 3x if 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) = x^4 - x²+1 b. h (-1)

In Exercises 31–32, the domain of each piecewise function is (-∞, ∞) (a) Graph each function. (b) Use the graph to determine the function's range.

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x^4 - x²+1 c. h (-x)

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3 a. f(-6)

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b). midpoint (-9, 8), endpoint (-16, 9)

In Exercises 41–46, use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. y=(1/2)x-2

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation. The y-value is the difference between four and twice the x-value.

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 necessary change(s) to produce a true statement. The ordered pair (2, 5) satisfies 3y - 2x = - 4.

In Exercises 77–92, use the graph to determine a.the x-intercepts, if any; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

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 origin, or none of these. |y| = -x

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 (2) · g (−1) .

You invested $20,000 in two accounts paying 1.45% and 1.59% annual interest. If the total interest earned for the year was $307.50, how much was invested at each rate?

You invested $30,000 in two accounts paying 2.19% and 2.45% annual interest. If the total interest earned for the year was $705.88, how much was invested at each rate?

A new car worth $36,000 is depreciating in value by $4000 per year. a. Write a formula that models the car's value, y, in dollars, after x years. b. Use the formula from part (a) to determine after how many years the car's value will be $12,000. c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.

A new car worth $45,000 is depreciating in value by $5000 per year. a. Write a formula that models the car's value, y, in dollars, after x years. b. Use the formula from part (a) to determine after how many years the car's value will be $10,000. c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.