3. parallel: (b) and (c); perpendicular (a) and (b), (a) and (c)

Transcription

1 SECTION Plot the points (0, 4), ( 2, 3), (1.5, 1), and ( 3, 0.5) in the Cartesian plane. 2. Simplify the expression Use the 3 lines whose equations are given. Which are parallel? Which are perpendicular? (a) y = 4 3 x 7 (b) y = 3 4 x + 1 (c) y = 3 4 x 4 1. Find the slope of the line passing through ( 3, 4) and (2, 2). 2. Find an equation of the line passing through (2, 7) and (5, 1). 3. Find the slope and y-intercept of y = 4x Find the equation of a line that passes through the point (0, 0) and is parallel to the line y = 1 3 x + 3. ANSWERS WU parallel: (b) and (c); perpendicular (a) and (b), (a) and (c) 1

2 QUIZ y = 2x slope 4, y-intercept 1 4. y = 1 3 x 2

3 SECTION Simplify the expression (2x + 1) 2 4(2x + 1) Determine whether the ordered pair ( 2, 0) is a solution of the equation y = 4 x Solve 4 + 3x x 2 = Let A = { 3, 1, 0, 2, 5} and B = { 2, 1, 1, 2, 3}. Does the set {( 3, 1), (0, 3), ( 1, 1), (2, 3)} represent a function from A to B? 2. Evaluate f( 0.5) for f(x) = x 4x Find the domain of the function f (x) = 3 2x 2 4x. ANSWERS WU 1. 4x 2 4x yes 3. [ 1, 4] QUIZ 1. yes all real numbers x except x = 0, 2 3

4 SECTION Find f( x) for f(x) = x Find the domain of the function g(x) = 4 x Evaluate the function when x = 7. x + 2, x > 5 f (x) = 4, x 5 4. A company produces a product for which the variable cost is $1.35 per unit and the fixed costs are $678. The total cost C for producing x units of the product can be represented by the function C(x) = 1.35x Find the total cost when 1000 units are produced. 1. Find the domain and range of the function whose graph is shown. 2. Use the vertical line test to determine whether the graph represents y as a function of x. 1 x, x < 1 3. Graph the function f (x) =. 2x + 3, x 1 4

5 4. Determine the intervals over which the function f(x) = x 2 is increasing, decreasing, or constant. 5. Determine whether the function g(x) = 1 is odd, even, or neither. 2 x ANSWERS WU 1. f( x) = x all real numbers x except x = $2028 QUIZ 1. domain: [ 5, 5); range: [ 2, 5] 2. y is a function of x increasing on (, 0); decreasing on (0, ) 5. even 5

6 SECTION 1.4 Determine whether the function is odd, even, or neither. 1. f(x) = x 3 4x 2. g(x) = 2x Find a relative minimum of the function f(x) = x 2 2x Graph the function f (x) = x Identify the parent function and the transformation shown in the graph. Then write an equation for the function shown in the graph. Identify the parent function f. Then describe the graph of the function g relative to the graph of f. 3. g(x) = 8x 3 4. g(x) = x

7 ANSWERS WU 1. odd 2. even 3. relative minimum (1, 4) QUIZ The graph is a vertical shift 3 units downward and a horizontal shift 1 unit to the right of the graph of f(x) = x 2 ; g(x) = (x 1) f(x) = x 3 ; Relative to the graph of f, the graph of g is a vertical stretch (each y-value is multiplied by 8) of the graph of f. 4. f(x) = x ; Relative to the graph of f, the graph of g is a horizontal shift 2 units to the left followed by a reflection in the x-axis and a vertical shift 4 units upward of the graph of f. 7

8 SECTION 1.5 Perform the operations and simplify. 1. (x 2 8x + 1) + (5x 7) 2. (4x 3 + x 2) (x 3 + 6x 2 + x) 3. (x 3)(x 2 + x) Find f(3x 2) for f(x) = 1 x 2. x 3 x 2 9 x x 2 5x + 6 Find (f + g)(x), (f g)(x), (fg)(x), and (f/g)(x). 1. f(x) = 4x 5, g(x) = (2 x) 2. f (x) = 2 x 2, g(x) = x x 1 3. Let f(x) = x 2 x + 6 and g(x) = 2x 3. Find f og, and give the domain. ANSWERS WU 1. x 2 3x x 3 6x x 3 2x 2 3x x x 3 QUIZ 1. (f + g)(x) = 3x 3; (f g)(x) = 5x 7; (fg)(x) = 4x x 10; (f/g)(x) = 4x 5 2 x, x 2 x 2 (x 2) x (f + g)(x) = x 3 + 2x 2 x 2 (x 1), x 0, 1; (f g)(x) = x 3 + 2x 2 x 2 (x 1), x 0, 1; (fg)(x) = 2 x(x 1), x 0, 1; (f / g)(x) = 2(x 1) x 3, x x 2 14x + 18 ; all real numbers x 8

9 SECTION 1.6 Given that f(x) = 4x 2 6x and g(x) = 1 x, find the composition f og 2. g of 3. Solve x = 2y + 3 y 1 for y. Find the inverse of the function. 1. f (x) = 1 3 x 2 2. f (x) = x + 4 x 6 3. Is the function shown in the graph a one-to-one function? Does it have an inverse function? Explain. 9

10 ANSWERS WU 1. x 2 3x 2. 2x 2 3x 3. y = x + 3 x 2 QUIZ 1. f 1 (x) = 3x f 1 (x) = 6x + 4 x 1 3. No; It does not pass the horizontal line test. Because the function is not one-to-one, it has no inverse function. 10

11 SECTION Solve 30 = k(0.2) 0.5 for k. 2. Let s = 3p 3 t. Find s when p = 1 3 and t = A small business purchases a piece of equipment for $13,350. After 10 years the equipment will have to be replaced. Its value at that time is expected to be $1820. Write a linear equation giving the value, V, of the equipment during the 10 years it will be used. Does the data show a positive correlation, negative correlation, or no correlation? Does the relationship between x and y appear to be linear? Sketch a scatter plot of the data. Use the regression feature of a graphing calculator to find a linear model for the data. x y

12 ANSWERS 2 WU V = 1153t + 13,350 9 QUIZ 1. No correlation. The relationship between x and y is not linear. (While there is a pattern, it is not linear. As x increases, y may increase or decrease.) 2. Negative correlation. The relationship between x and y is linear. 3. The equation y = 0.002x models the data. 12