Use the graphs of f and g to answer the following. (a) Identify the domains and ranges of f and g. Domain of f : [−4, 4] [−3, 5] [−3, 3] [−2, 3] Range of f : [−2, 3] [−4, 4] [−3, 5] [−3, 3] Domain of g : [−2, 3] [−4, 4] [−3, 5] [−3, 3] Range of g : [−2, 3] [−3, 5] [−4, 4] [−3, 3] (b) Identify f(−3) and g(−3). f(−3) = g(−3) = (c) For what value(s) of x is f(x) = g(x) ? x = (d) Estimate the solution(s) of f(x) = 2. x = (e) Estimate the solutions of g(x) = 0. x = (smallest value) x = (smallest value)
Evaluate (if possible) the function at the given values of the independent variable. Simplify the results. (If an answer does not exist, enter DNE.) g(x) = x2(x−2) (a) g(2) = (b) g(3/2) = (c) g(c) = (d) g(t+2) =
Evaluate the function at the given value of the independent variable. Simplify the results. (If an answer is undefined, enter UNDEFINED. ) f(x) = x3−49 x f(x)−f(7) x−7 =
Evaluate (if possible) the function at the given value(s) of the independent variable. Simplify the results. f(x) = x3 − 36 x f(x)−f(6) x−6
Find the domain and the range of the function. h(x) = −x+2 Domain: (−∞, ∞) [−2, ∞) (−∞, 2] (−∞, 0] [0, ∞) Range: (−∞, ∞) [−2, ∞) (−∞, 2] (−∞, 0] [0, ∞)
Find the domain of the function. g(x) = 7 1−cosx all x = nπ, where n is an integer all x ≠ 7nπ, where n is an integer (−∞, −π)∪(−π, ∞) (−∞, ∞) all x ≠ 2nπ, where n is an integer
Consider the following. f(x) = 16 − x2 Sketch the graph of the function. Use a graphing utility to verify your graph. Find its domain and range. Domain: [−4, 4] [0, 4] (−∞, 0)∪(4, ∞) (−∞, ∞) (−∞, −4)∪(4, ∞) Range: (−∞, 0)∪(4, ∞) (−∞, −4)∪(4, ∞) [0, 4] [−4, 4] (−∞, ∞)
Consider the following. g(t) = 4 sinπt Sketch a graph of the function. Use a graphing utility to verify your graph. Find its domain and range. Domain: (−∞, 0)∪(0, ∞) [−4, 4] (−∞, ∞) [−π, π] (−∞, 4)∪(4, ∞) Range: [−4, 4] (−∞, ∞) (−∞, 4)∪(4, ∞) [−1, 1] [−π, π]
Use the vertical line test to determine whether y is a function of x. Yes, y is a function of x. No, y is not a function of x. It cannot be determined whether y is a function of x. y = {x − 3, x ≤ 0 −x + 3, x > 0
Determine whether y is a function of x. x3 + y = 9 Yes, y is a function of x. No, y is not a function of x. It cannot be determined whether y is a function of x.
Use the graph of y = f(x) to match the function with its graph. y = f(x + 6) + 2 a b c d e g
Given f(x) = sinx and g(x) = πx, evaluate each expression. (a) f(g(2)) (b) f(g(1/2)) (c) g(f(0)) (d) g(f(π/4)) (e) f(g(x)) (f) g(f(x))
Test for symmetry with respect to each axis and to the origin. (Select all that apply. ) y = x8 x2+1 The equation is symmetric with respect to the x-axis. The equation is symmetric with respect to the y-axis. The equation is symmetric with respect to the origin. None of the above. Identify the intercept. (x, y) = ( ) Test for symmetry. (Select all that apply.) The equation is symmetric with respect to the x-axis. The equation is symmetric with respect to the y-axis. The equation is symmetric with respect to the origin. None of the above.
Use a graphing utility to graph the equation. Identify the intercepts. y2−x = 25 x-intercept (x, y) = ( ) y-intercepts (x, y) = () (smaller y-value) (x, y) = ( ) (larger y-value) Test for symmetry. (Select all that apply. ) The equation is symmetric with respect to the x-axis. The equation is symmetric with respect to the y-axis. The equation is symmetric with respect to the origin. None of the above.
Two equations and their graphs are given. Find the intersection points of the graphs by solving the system. {x2 + y = 1 x − 2y = 8 (x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value) Find all solutions of the system of equations. (If there is no solution, enter NO SOLUTION. ) {y = 4 − x2 y = x2 − 4(x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value)