Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. 27. x2 + y2 = 49 Down 3, left 2 28. x2 + y2 = 25 Up 3, left 4 29. y = x3 Left 1, down 1 30. y = x^(2/3) Right 1, down 1 31. y = sqrt(x) Left 0.81 32. y = -sqrt(x) Right 3 33. y = 2x - 7 Up 7 34. y = 1 /2 (x + 1) + 5 Down 5, right 1 35. y = 1/x Up 1, right 1 36. y = 1/x2 Left 2, down
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.
27. x2 + y2 = 49 Down 3, left 2
28. x2 + y2 = 25 Up 3, left 4
29. y = x3 Left 1, down 1
30. y = x^(2/3) Right 1, down 1
31. y = sqrt(x) Left 0.81
32. y = -sqrt(x) Right 3
33. y = 2x - 7 Up 7
34. y = 1 /2 (x + 1) + 5 Down 5, right 1
35. y = 1/x Up 1, right 1
36. y = 1/x2 Left 2, down
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