Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x + 1)² + y² = 25

In Exercises 51–54, graph the given square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of x that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = √x (x = 0, 1, 4, 9) and g(x) = √x −1 (x = 0, 1, 4, 9)

In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = ∛x + 1

Use the graph of y = f(x) to graph each function g. g(x)=2f(x-1)

In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. f(g(1))

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+6x+2y+6 = 0

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. g(x) = x² - 2

Find

a. (fog) (x)

b. (go f) (x)

c. (fog) (2)

d. (go f) (2).

f(x) = x+4, g(x) = 2x + 1

In Exercises 51–54, graph the given square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of x that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = √x (x = 0, 1, 4, 9) and g (x) = √(x + 2) (x = = −2, −1, 2, 7)

Find the average rate of change of f(x) = x^2 - 4x from x_1 = 5 to x_2 = 9.

Use the vertical line test to identify graphs in which y is a function of x.

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. g(x) = (x − 2)²

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² – 10x – 6y – 30 = 0

In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. (go f) (-1)

In Exercises 55–59, use the graph of to graph each function g.

g(x) = f(x + 2) + 3

Graph each equation in a rectangular coordinate system. f(x) = 1

Find a. (fog) (x) b. (go f) (x) f(x)=4x-3, g(x) = 5x² - 2

Find a. (fog) (2) b. (go f) (2) f(x)=4x-3, g(x) = 5x² - 2

Graph each equation in a rectangular coordinate system. 3x -18=0

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. h(x) = -(x − 2)²

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+8x-2y-8=0

Use the vertical line test to identify graphs in which y is a function of x.

Find a. (fog) (x) b. (go f) (x) f(x) = x²+2, g(x) = x² – 2

Find a. (fog) (2) b. (go f) (2) f(x) = x²+2, g(x) = x² – 2

Use the vertical line test to identify graphs in which y is a function of x.

Let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. (fog) (0)

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² - 2x + y² – 15 = 0

Use the vertical line test to identify graphs in which y is a function of x.

Find a. (fog) (x) b. (go f) (x) f(x) = 4-x, g(x) = 2x² +x+5