10-5 Graphing Square Root Functions

Quick Review

Graph a square root function by plotting points or translating the parent square root function y = x . y equals square root of x , .

The graphs of y = x + k y equals square root of x plus k  and y = x − k y equals square root of x minus k  are vertical translations of y = x . y equals square root of x , .  The graphs of y = x − h y equals , square root of x minus h end root  and y = x + h y equals , square root of x plus h end root  are horizontal translations of y = x . y equals square root of x , .

Example

What is the graph of the square root function y = x − 2 y equals , square root of x minus 2 end root ?

The graph of y = x − 2 y equals , square root of x minus 2 end root  is the graph of y = x y equals square root of x  shifted 2 units right.

Exercises

Find the domain of each function.

46. y = x − 5 y equals square root of x minus 5
47. y = x + 4 y equals , square root of x plus 4 end root

Graph each function.

48. y = x + 6 y equals square root of x plus 6
49. y = x − 8 y equals , square root of x minus 8 end root
50. y = x − 2.5 y equals . square root of x minus 2.5 end root
51. y = 1 4 x y equals , 1 fourth , square root of x
52. y = 3 x y equals 3 square root of x

10-6 Trigonometric Ratios

Quick Review

You can use the sine, cosine, and tangent ratios to find the measurements of sides or angles of right triangles.

sin   A = opposite leg hypotenuse cos   A = adjacent leg hypotenuse tan   A = opposite leg adjacent leg table with 3 rows and 1 column , row1 column 1 , sine eh equals . fraction oppositeleg , over hypotenuse end fraction , row2 column 1 , cosine eh equals . fraction adjacentleg , over hypotenuse end fraction , row3 column 1 , tangent eh equals . fraction oppositeleg , over adjacentleg end fraction , end table

Example

What are the trigonometric ratios of angle A?

sin   A = 3 13 = 3 13 13 cos   A = 2 13 = 2 13 13 tan   A = 3 2 table with 3 rows and 2 columns , row1 column 1 , sine eh , column 2 equals , fraction 3 , over square root of 13 end fraction , equals . fraction 3 square root of 13 , over 13 end fraction , row2 column 1 , cosine eh , column 2 equals , fraction 2 , over square root of 13 end fraction , equals . fraction 2 square root of 13 , over 13 end fraction , row3 column 1 , tangent eh , column 2 equals , 3 halves , end table

Exercises

Find the trigonometric ratios for ∠ A . angle cap a .

Suppose a right triangle ABC has right angle C. Find the measures of the other sides to the nearest tenth.

56. length of A B ¯   =   12 , eh b bar , equals 12 comma  measure of ∠ A   =   34 ° angle . eh equals 34 degrees
57. length of A C ¯   =   8 , eh c bar , equals 8 comma  measure of ∠ B   =   52 ° angle . b equals 52 degrees
58. length of B C ¯   =   18 , b c bar , equals 18 comma  measure of ∠ A   =   42 ° angle . eh equals 42 degrees
59. length of A B ¯   =   25 , eh b bar , equals 25 comma  measure of ∠ A   =   12 ° angle . eh equals 12 degrees

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