2. Graphs of Equations

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 graph, tick marks along the axes represent one unit each.

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)=4x+5 b. f(x + 1)

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) = x² + 2x + 3 a. g(-1)

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.

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=√(4x+1)

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.

In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x)= |x|, g(x) = |x| +1

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation. The y-value is three decreased by the square of the x-value.

In Exercises 47–50, write each English sentence as an equation in two variables. Then graph the equation. y = 5 (Let x = -3, - 2, - 1, 0, 1, 2, and 3.)

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. 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.

In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).] y = 2(x + 2)^2 + 5(x + 2) - 3

In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).] y = x^(-2) - x^(-1) - 6

In Exercises 85–90, find the x-intercepts of the graph of each equation. Then use the x-intercepts to match the equation with its graph. [The graphs are labeled (a) through (f).] y = √(x - 4) + √(x + 4) - 4

Write an equation involving absolute value that says the distance between p and q is 2 units.