Linear Relations Study Guide Topic: Mapping and Relations 1. Write the ordered pairs that represents the relation in the mapping below. 2. Express the relation {( -­‐4, -­‐1), (-­‐1,2), (1, -­‐4), (2,-­‐3), (4,3)} as a table, a graph and a mapping. Then state the domain and range. Topic: Functions Determine the domain and range of each of the relations below. Then determine if the relation is a function or not a function. Justify your answers for each question. Linear Relations Study Guide Topic: Function Notation 1. Let 𝑔(𝑥 ) = −5𝑥 + 2. Evaluate each of the following: a. g( -­‐ 1) b. g( -­‐ 2) c. g(x) = 12 d. g(x) = 17 2. Suppose 𝑓(𝑡) = 7𝑡 + 4. a. Determine t such that 𝑓(𝑡) = 0. b. Evaluate 𝑓(0) 3. Use the table to the right to find the following: X 1 (
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a. x when 𝑓 𝑥 = 25 2 b. 𝑓 (3) =? 3 c. x when 𝑓(𝑥 ) = 4 4 5 4. Use graph of f(x) to the right to find the following: a. 𝑓(– 4) b. 𝑓(0) c. 𝑓(3) -5
d. 𝑓(−5) e. x when 𝑓(𝑥) = 2 f. x when 𝑓(𝑥) = 0 Y 1 4 9 16 25 f(x) 5
y
5
-5
x
Linear Relations Study Guide Topic: Graphs of Linear Functions 1. Find the slope for each of the lines below. d) a) b) c) e) 2. Write the equation of each of the lines given on the graph below in slope intercept form (y = mx+c). 3. Graph the following lines. 4
a) 𝑦 = 5 𝑥 + 4 b) 𝑦 = −3𝑥 + 7 c) 𝑦 = 5 d) 𝑥 = −3 Topic: Writing Linear Functions Linear Relations Study Guide Use the graph below to find the equation of the lines passing through 2 points. For each of these questions, start from point-­‐slope form 𝑦 − 𝑦6 = 𝑚(𝑥 − 𝑥6 ). Find the slope of line AC. Find the slope of line BD. Write the equation of for the line AC in the form 𝑎𝑥 + 𝑏𝑦 + 𝑑 = 0 (standard form). Rearrange your answer from 1) so that your equation is in the form 𝑦 = 𝑚𝑥 + 𝑐 (slope-­‐intercept form). Write the equation of for the line BD in the form 𝑎𝑥 + 𝑏𝑦 + 𝑑 = 0. Rearrange your answer from 3) so that your equation is in the form 𝑦 = 𝑚𝑥 + 𝑐 (slope-­‐intercept form). Topic: Parallel and Perpendicular Lines 1. Write the equation of the line parallel to 𝑦 = 2𝑥 − 4 and passing through the point (2, -­‐ 1). 2. Write the equation of the line perpendicular to 𝑦 = 4 and passing through the point (-­‐ 1, 8). 3. Write the equation of the line parallel to 𝑥 = 3 and passing through the point (-­‐1, 8) 4. Write the equation of the line perpendicular to 𝑦 = 2𝑥 − 4 and passing through the point (2, -­‐ 1). Topic: Linear Modeling with Arithmetic Sequences 1. For the sequence of numbers: 18 13 8 3 …… -­‐37 -­‐42 a) Write down the common difference. b) Find the general rule. c) Find the tenth term. d) Find the number of terms in the sequence. 2. For the sequence of numbers: -­‐29 -­‐2 25 …… a) Show that the sequence is arithmetic. b) Write down the common difference c) Find the general rule. d) Determine if 345 is a member of the sequence. Topic: Linear Modeling with Regressions 1. 2. 3. 4. 5. 6. Linear Relations Study Guide 1. The table of values shows the cost of renting DVDs at a video store. What is the independent variable? What is the dependent variable? 2. Graph the data on the grid provided. Be sure to label the axes. 3. 4. 5. 6. Write the equation of the line of best fit. Plot this equation on the graph above (be sure to label the y-­‐intercept). Predict the cost of renting 10 DVDs. Predict the number of DVDs that will cost $72.