<p> Transformations of Exponential Functions - Worksheet</p><p>1. Graph each set of functions on the same axes by applying the appropriate transformations. x a) 骣1 b) x f( x ) = 琪 p( x )= 5 桫3 1 -x x-1 q( x )= (5 ) 骣1 4 g( x )= - 2琪 桫3 r( x )= 50.25x + 3 2x 骣1 h( x )=琪 - 4 桫3 2. For each transformation below, state the base (parent) function and then describe the transformations in the order in which they should be applied. 2x x+1 骣1 a) f( x )= - 3(4 ) b) g( x )= 2琪 + 3 桫2 1 c) h( x )= (0.5x-4 ) - 1 d) k( x )= 5-3x - 6 7</p><p>3. Let f( x )= 4x . For each function that follows,  State the transformations in the order that they that must be applied to f(x)  Create an equation of the transformed functions below (using the base (parent) function)  State the y-intercept and the equation of the asymptote  Sketch the new function  State the domain and range</p><p>1 a) g( x )= f ( - x ) + 2 b) h( x )= - 2 f (2 x - 6) 2 骣 1 c) j( x )= - f (0.25 x + 1) - 1 d) k( x )= f琪 - x + 2 桫 2</p><p>4. a) Compare the functions f( x )= 9x and g ( x ) = 32 x . b) Use exponent laws to explain what you found in part a).</p><p>Answers: x x 骣1 2. a) y = 4 ; v.s. of 3, reflect in x-axis, translate left 1 b) y = 琪 ; v.s. of 2, h.c. of ½ , translate up 3 桫2 x 骣1 x 1 x 1 c) y = 琪 OR y = 0.5 ; v.c. of , translate right 4, translate down 1 d) y = 5 ; h.c. of , reflection in y-axis, translate left 2 桫2 7 3 1 3. a) v.c. of ½ , reflection in y-axis, translate up 2; g( x )= (4-x ) + 2 ; (0, 2.5) and y = 2; D:{xЄR}, R:{yЄR | y > 2) 2 b) v.s. of 2, h.c. of ½, reflection in x-axis, translate right 3; h( x )= 2(42x- 6 ) ; (0, 0.00049) and y = 0; D:{xЄR}, R:{yЄR | y < 0} (0.25x 1) c) h.s. of 4, reflection in x-axis, translate left 4, translate down 1; j( x )= - 4+ - 1; (0, -5) and y = -1; D:{xЄR}, R:{yЄR | y > -1} 1 (-x + 2) d) h.s. of 2, reflection in y-axis, translate right 4; k( x )= 4 2 ; (0, 16) and y = 0; D:{xЄR}, R:{yЄR | y > 0}</p><p>4. a) f(x) = g(x) b) f( x )= 9x f( x )= (32 )x write 9 in another form that means the same thing f( x )= 32x use 'power of a power' exponent law to combine exponents \f( x ) = g ( x )</p>