3.1-3.5 Review Notebook PDF

## 3.1-3.5 Review.notebook ### Determine whether the relation is a function. - (1, 2), (2, 1), (3, 6), (4, 13), (5, 22) - (7, 4), (5, 1), (3, -8), (1, -5), (3, 6) | Input, x | Output, y | |---|---| | 16 | -2 | | 1 | -1 | | 0 | 0 | | 1 | 1 | | 16 | 2 | | Input, x | Output, y | |---|---| | -3 | 11 |...

## 3.1-3.5 Review.notebook ### Determine whether the relation is a function. - (1, 2), (2, 1), (3, 6), (4, 13), (5, 22) - (7, 4), (5, 1), (3, -8), (1, -5), (3, 6) | Input, x | Output, y | |---|---| | 16 | -2 | | 1 | -1 | | 0 | 0 | | 1 | 1 | | 16 | 2 | | Input, x | Output, y | |---|---| | -3 | 11 | | 0 | 5 | | 3 | -1 | | 6 | -7 | | 9 | -13 | ### Modeling with Mathematics The function $y = 3.5x + 2.8$ represents the cost y (in dollars) of a taxi ride of x miles. a. Identify the independent and dependent variables. b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function. ### Determine whether the graph is a linear or nonlinear function. ### Determine whether the table is a linear or nonlinear function. | x | y | |---|---| | 1 | 5 | | 2 | 10 | | 3 | 15 | | 4 | 20 | | x | y | |---|---| | 4 | 16 | | 8 | 12 | | 12 | 7 | | 16 | 1 | | x | y | |---|---| | 5 | -9 | | 7 | -3 | | 9 | -1 | | 11 | 3 | | x | y | |---|---| | -1 | 35 | | 0 | 20 | | 1 | 5 | | 2 | -10 | ### Determine whether the equation is a linear or nonlinear function. - $y = x^2 + 13$ - $y = \sqrt{8} - x$ - $2 + \frac{1}{2}y = 3x + 4$ - $18x - 2y = 26$ - $y = 7 - 3x$ - $y = 4x(8 -x)$ - $y - \frac{2}{3}x = 2x - \frac{5}{3}y $ - $2x + 3y = 9xy$ ### In Exercises 27 and 28, find the domain of the function represented by the graph. Determine whether the domain is discrete or continuous. Explain. #### 27. * Domain: 4, 8, 12 * Discrete #### 28. * Domain: 0 through 8 * Continuous ### Modeling with Mathematcs The number y of calories burned after x hours of rock climbing is represented by the linear function $y = 650x$. Find the domain of the function. Is the domain discrete or continuous? Explain. ### Does the table represent a linear or nonlinear function? Explain. | Time (hours), t | Distance(miles), d | |---|---| | 1 | 60 | | 3 | 180 | | 5 | 310 | ### Evaluate the function. - $f(x) = 18 - 0.5x$ - $g(x) = x - 4$ - $h(x) = 2x^2 - 3x + 9$ - $f(10)$ - $g(-5)$ - $h(-1)$ - $g(3) - 10$ - $h(0) + g(-3)$ - $f(6) - g(19)$ ### Solve for x. - $m(x) = 4x + 15; m(x) = 7$ - $j(x) = -\frac{4}{5}x + 7; j(x) = -5$ ### Find the value of x so that $f(x) = 5$. * $x = 3$ ### Find the value of x so that $f(x) = 6$. * $x = 1.5$ ### The function $m = 30 - 3r$ represents the amount m (in dollars) of money you have after renting r video games. a. Identify the independent and dependent variables. b. Find the domain and range of the function. Is the domain discrete or continuous? Explain. ### The function $d(x) = 1375 - 110x$ represents the distance (in miles) a high-speed train is from its destination after x hours. a. How far is the train from its destination after 8 hours? b. How long does the train travel before reaching its destination? ### Graph. - $y = -2$ - $x = -3$ ### Find the x-intercept and the y-intercept. - $3x - 5y = 30$ - $2x + 4y = -8$ - $6x - 3y = 6$ - $y = 2x - 4$ - $x = -1$ - $y = 8$ ### Graph. - $2x - 3y = 12$ - $6x + 4y = -12$ ### Modeling with Mathematics You are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts. The equation $10x + 12y = 300$ models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts. a. Graph the equation. Interpret the intercepts. b. Twelve students decide they want short-sleeved shirts. How many long-sleeved shirts can you order? ### Find the slope of the line. - (-3, 1) and (2, -2) - (-2, 2) and (2, -3) - (0, 3) and (5, -1) - x | y - -9 | -2 - -5 | 0 - -1 | 2 - 3 | 4 - x | y - -1 | -6 - -2 | -6 - -5 | -6 - -8 | -6 - x | y - 0 | -4 - 0 | 0 - 0 | 4 - 0 | 8 ### Find the slope of the line through the points. - (-3, -2) and (6, 8) - (-1, -1) and (-8, -15) - (5, 3) and (10, 3) ### Identify the slope and y-intercept. - y = 3x - 5 - 2x + y = 8 - 3x - 4y = 12 ### Graph. - y = -x + 5 - $y = \frac{1}{2}x - 3$ - $y = \frac{7}{5}x$ - y + 5 = 3x