Intermediate Algebra. Quiz

Intermediate Algebra Quiz #3 NAME: KEY Graph the following functions. Clearly label at least 3 points. A) f(x) = 3 - x [y = -x + 3] [Graph of a linear function with slope -1 and y-intercept 3] B) g(x) = -3 [y = -3] [Graph of a horizontal line at y = -3] Two relationships are given below. State which relationships are functional. In each situation, give a brief explanation why you decided it was a function.   A) x² + 2xy + y² = 16 x₀ = 0 → (0)² + 2(0)y + y² = 16 y² = 16 y = ±4 NOT A FUNCTION (Two outputs for one input) B) [Graph of a parabola] NOT A FUNCTION (Vertical line test fails) Clearly state what the DOMAIN is for the function shown below. Show your work or explain how you got your answer. f(x) = (x + 4) / (5x - 3) 5x - 3 ≠ 0 5x ≠ 3 x ≠ 3/5 Domain: (-∞, 3/5) U (3/5, ∞) 4. Determine the DOMAIN and the RANGE for each function shown below. Clearly state which set is the domain and which is the range. A) D: {-5, -4, -2, 0, 2, 3, 4} R: {1, 2, 3, 4} B) D: [-5, 5] R: [-1, ∞) 5. Given the function f(x) = x² + 4, determine the following: A) f(-2) = (-2)² + 4 = 8 B) f(x) + 5 = (x² + 4) + 5 = x² + 9 C) f(a + 1) = (a + 1)² + 4 = a² + 2a + 1 + 4 = a² + 2a + 5 D) f(x) = 16 * x² + 4 = 16 * x² = 12 * x = ±√12 6. A table representing the function h(x) is shown, use it to do the following: A) Find: h(-2) = 5 B) Find: h(x) = 1 * x = -4 * x = 0 8. A graph of the function f(x) is shown, use it to do the following: A) Find f(4) = 4 B) Find f(-2) + 5 = -2 + 5 = 3 C) Solve f(x) = 0 * x = -5, -3, 3 D) Solve (f(2) - f(-4)) / (2 - (-4)) = (-2 - 1) / 6 = -3/6 = -1/2 4. Determine the DOMAIN and the RANGE for each function shown below. Clearly state which set is the domain and which is the range. A) D: {-5, -4, -2, 0, 2, 3, 4} R: {1, 2, 3, 4} B) D: [-5, 5] R: [-1, ∞) 5. Given the function f(x) = x² + 4, determine the following: A) f(-2) = (-2)² + 4 = 8 B) f(x) + 5 = (x² + 4) + 5 = x² + 9 C) f(a + 1) = (a + 1)² + 4 = a² + 2a + 1 + 4 = a² + 2a + 5 D) f(x) = 16 * x² + 4 = 16 * x² = 12 * x = ±√12 6. A table representing the function h(x) is shown, use it to do the following: A) Find: h(-2) = 5 B) Find: h(x) = 1 * x = -4 * x = 0 8. A graph of the function f(x) is shown, use it to do the following: A) Find f(4) = 4 B) Find f(-2) + 5 = -2 + 5 = 3 C) Solve f(x) = 0 * x = -5, -3, 3 D) Solve (f(2) - f(-4)) / (2 - (-4)) = (-2 - 1) / 6 = -3/6 = -1/2