algebra study guide 7

No Work ⇔ No Points Use Pencil Only ⇔ Be Neat & Organized 1. (3 points) Write 4x − 5y = 15 in slope-intercept form, then express your answer in function notation. 1. 2. (8 points) Graph both linear functions in each system, clearly mark intercepts, rise and run of the slope, or any point used in the graph: 2 x−2 3 −3 g(x) = x 2 f (x)= f (x) = 2x − 3 g(x) = 3 y y x Page 1 of 4 Study Guide 7 x Total Points: 50 3. Consider the function f (x) = x2 − 4, (a) (1 point) Find f (0). (a) (b) (1 point) Find f (−2). (b) (c) (3 points) Find the difference quotient f (x + h) − f (x) h . (c) x−4 4. Consider the function f (x) = x+2 , (a) (2 points) Find f (4). (a) (b) (2 points) Find f (−2). (b) 5. Consider the function f (x) = |x − 1| − 1 , (a) (1 point) Find f (0). (a) (b) (1 point) Find f (2). (b) Page 2 of 4 Study Guide 7 Total Points: 50 6. Consider the following relation: (a) (2 points) Find its domain. (a) (b) (2 points) Find its range. (b) (c) (2 points) Is this relation a function? Justify your answer. (c) 7. Consider t he graph below: 3 2 1 -5 -4 -3 -2 -1 0 -1 0 1 2 3 4 5 -2 -3 (a) (2 points) Give its domain in interval notation. (a) (b) (2 points) Give its range in interval notation. (b) (c) (2 points) Use the graphing area above to draw a new graph by shifting the given graph one unit left, then two units down. Page 3 of 4 Study Guide 7 Total Points: 50 8. Consider the graph below: 7 6 5 4 3 2 1 0 1 2 (a) (2 points) Give its domain in interval notation. (a) (b) (2 points) Give its range in interval notation. (b) (c) (2 points) Does this graph belong to a function? Justify your answer. (c) (d) (2 points) Give any y−intercept. (d) (e) (2 points) Give any x−intercept. (e) 9. Algebra Review Problems: 2 (a) (2 points) Factor 3x − 16x − 35. (a) (b) (2 points) Solve (3x + 5)(x − 7) = 0 by using the zero-factor theorem. 2 2 (b) (c) (2 points) Simplify (3x − 5) − (3x + 5) . (c) Page 4 of 4 Study Guide 7 Total Points: 50