Study Sheet - Midterm 1 (Functions, Limits, Asymptotes & Continuity) Questiions - 1 1.1 Study Sheet(midterm I Some formulas distance formula:The

Study Sheet - Midterm 1 (Functions, Limits, Asymptotes & Continuity) Questiions

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1 Study Sheet(midterm I) 1.1 Some formulas : distance formula :The distance d between ( x 1 , y 1 ) , ( x 2 , y 2 ) is d = p ( x 1 - x 2 ) 2 + ( y 1 - y 2 ) 2 midpoint formula :The midpoint of ( x 1 , y 1 ) , ( x 2 , y 2 ) is ( ( x 1 + x 2 2 , y 1 + y 2 2 ) Formula of a circle: The formula of a circle centered at ( a, b ) with radius r is ( x - a ) 2 + ( y - b ) 2 = r 2 point-slope form of a line : The formula of a line going through ( x 1 , y 1 ) with slope m is y - y 1 = m ( x - x 1 ) slope-intercept form of a line : The formula of a line with a slope m and y - intercept (0 , b ) is y = mx + b slope of a line : The slope of a line going through ( x 1 , y 1 ) , ( x 2 , y 2 ) is m = y 1 - y 2 x 1 - x 2 Parallel and perpendicular lines: (1) Two distinct nonvertical lines are parallel if and only if their slopes are equal, say m 1 = m 2 . (2) Two nonvertical lines are perpendicular if and only if their slopes satisfy m 1 m 2 = - 1 x- and y- intercept: The x-intercepts of f ( x ) are points in the form of ( c, 0), where f ( c ) = 0. The y-intercepts of f ( x ) are points in the form of (0 , b ), where b = f (0). Exercises: (1) :Find the x- and y- intercept of y = x 2 9 - x 2 . (2) :Find the formula of a circle centered at (2 , 3) with radius 5.