2. Graphs of Equations

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x⁴ - x²+1 c. h (-x)

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x⁴ - x² +1 d. h (3a)

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3 b. f(10)

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) = x², g(x) = x² - 2

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) = x³, g(x) = x³ +2

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)

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

Let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g(-1) and f(g(-1)).

Evaluate each function at the given values of the independent variable and simplify. g(x) = x² - 10x - 3 a. g(-1)

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. g(x) = x² - 10x - 3 b. g(x+2)

Evaluate each function at the given values of the independent variable and simplify. g(x) = x² - 10x - 3 c. g(-x)

Evaluate each function at the given values of the independent variable and simplify. h(x) = x⁴ - x²+1 a. h (2)

Evaluate each function at the given values of the independent variable and simplify. h(x) = x⁴ - x² +1 b. h (-1)

Evaluate each function at the given values of the independent variable and simplify. h(x) = x³ − x + 1 a. h (3)

Evaluate each function at the given values of the independent variable and simplify. h(x) = x³ − x + 1 b. h (-2)