2. Graphs of Equations

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = x³

Determine whether each equation defines y as a function of x. x+y³ = 8

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)

Determine whether each relation is a function. Give the domain and range for each relation. {(3, 4), (3, 5), (4, 4), (4, 5)}

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)

Evaluate each function at the given values of the independent variable and simplify. g(x) = 3x^2 - 5x + 2 (a) g(0), (b) g(-2), (c) g(x-1), (d) g(-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. h(x) = x³ − x + 1 a. h (3)

Use the graph of g to solve Exercises 71–76.

For what value of x is g(x) = 1?

Evaluate each function at the given values of the independent variable and simplify. $f\left(r\right)=\sqrt{r+6}+3$

$\text{a. }f(-6)$

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

Evaluate each function at the given values of the independent variable and simplify. h(x) = x⁴ - x²+1 a. h (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 + 2) (x = = −2, −1, 2, 7)

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.