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**Extra info for TExES Mathematics-Physics 8-12 143 Teacher Certification Test Prep Study Guide (XAM TEXES)**

**Sample text**

Its slope is 0 (zero). 1. Find the slope and intercepts of 3 x + 2y = 14 . 3 x + 2y = 14 = 2y − 3 x + 14 = y − 3 2 x +7 The slope of the line is − 3 2 , the value of m. The y intercept of the line is 7. The intercepts can also be found by substituting 0 in place of the other variable in the equation. To find the y intercept: let x = 0; 3(0) + 2 y = 14 0 + 2 y = 14 2 y = 14 y=7 (0,7) is the y intercept. MATHEMATICS-PHYSICS 8-12 34 To find the x intercept: let y = 0; 3 x + 2(0) = 14 3 x + 0 = 14 3 x = 14 x = 14 3 ( 14 3 ,0) is the x intercept.

Determine if log x3 = 3 log x for all values of x. x log x3 3 log x 1 0 0 10 3 3 100 5 5 The log x3 = 3 log x for all values of x. The functions form an identity and the graph of y = log x3 and y = 3 log x is identical. 5 y x 1 -5 MATHEMATICS-PHYSICS 8-12 32 10 100 TEACHER CERTIFICATION STUDY GUIDE Example 3: Consider the functions y = sin (x + π ) and y = cos x. Determine if 2 the functions represent an identity by graphing. Determine if sin (x + x π 2 ) = cos x for all values of x. 707 -1 -1 π 4 π π ) and y = cos x form an identity 2 because they are equal for all values of x.

F (x) = 7 f10) = 7 2. Same as above. Notice that both answers are equal to the constant given. A relation is any set of ordered pairs. The domain of the relation is the set of all first co-ordinates of the ordered pairs. ) The range of the relation is the set of all second co-ordinates of the ordered pairs. ) MATHEMATICS-PHYSICS 8-12 23 TEACHER CERTIFICATION STUDY GUIDE Practice Problems: { } 1. If A = ( x, y ) y = x 2 − 6 , find the domain and range. 2. Give the domain and range of set B if: { } B = (1, − 2),(4, − 2),(7, − 2),(6, − 2) 3.