# Transformations of Exponential Functions ```Transformations of Exponential Functions - Worksheet
1. Graph each set of functions on the same axes by applying the appropriate transformations.
x
a)
b) p ( x )  5 x
1
f ( x)   
3
1
g ( x )  2  
3
1 x
(5 )
4
r ( x)  50.25 x  3
q( x) 
x 1
2x
1
h( x )     4
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
1
3
2
a) f ( x)  3(4 x 1 )
c) h( x) 
b) g ( x)  2  
1
(0.5 x  4 )  1
7
d) k ( x)  53 x 6
3. Let f ( x)  4 x . 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
a) g ( x) 
1
f ( x)  2
2
b) h( x)  2 f (2 x  6)
 1

x  2
 2

d) k ( x)  f  
c) j ( x)   f (0.25 x  1)  1
4. a) Compare the functions f ( x)  9 x and g ( x)  32 x .
b) Use exponent laws to explain what you found in part a).
2.
a)
y  4 x ; v.s. of 3, reflect in x-axis, translate left 1
x
c) y   1  OR
 
2
3.
y  0.5x ; v.c. of
1 , translate right 4, translate down 1
7
x
b)
1
y 
2
d)
y  5 x ; h.c. of
; v.s. of 2, h.c. of &frac12; , translate up 3
1 , reflection in y-axis, translate left 2
3
a) v.c. of &frac12; , reflection in y-axis, translate up 2; g ( x)  1 (4 x )  2 ; (0, 2.5) and y = 2; D:{xЄR}, R:{yЄR | y &gt; 2)
2
b) v.s. of 2, h.c. of &frac12;, reflection in x-axis, translate right 3;
h( x)  2(42 x 6 ) ; (0, 0.00049) and y = 0;
c) h.s. of 4, reflection in x-axis, translate left 4, translate down 1;
d) h.s. of 2, reflection in y-axis, translate right 4;
4.
a) f(x) = g(x)
b)
j ( x)  4(0.25 x1)  1 ;
D:{xЄR}, R:{yЄR | y &lt; 0}
(0, -5) and y = -1; D:{xЄR}, R:{yЄR | y &gt; -1}
1
(  x  2)
2
; (0, 16) and y = 0; D:{xЄR}, R:{yЄR | y &gt; 0}
k ( x)  4
f ( x)  9 x
f ( x)  (32 ) x  write 9 in another form that means the same thing
f ( x)  32 x  use 'power of a power' exponent law to combine exponents
 f ( x)  g ( x)
```