Exercise 1.

Part I: Use the shifting/reflection techniques to graph the each of the following functions together with $f(x)=2^{x}$;.[Do them by hands first and verify your answers with a technology].

(1) $f_{1}(x)=2^{x}+2$;

(2) $f_{2}(x)=2^{x}-2$;

(3) MATH

(4) MATH

(5) MATH;

(6) MATH

Part II: Find the corresponding inverse functions for the functions above. [hint: Use the shiftings/reflections to find the corresponding inverses; for example if the original function is shifted up (down) then its inverse will be shifted right (left). If the orignial function is being reflected across $x-axis$ ( $y-axis),$then its inverse will be reflected across $y-axis$ ( $x-axis).$].

Exercise 2. Given f(x) = 3^x+2,

(a) Find g that is being horizontally shifted to the right 3 units from f.

(b) Find h that is being vertically shifted down 5 units from g.

Note: You should be able to do this by hand first and verify your answer with a technology.

Exercise3. Given MATH,

(a) Find $g$ that is being horizontally shifted to the right $3$ units from $f$.

(b) Find $h$ that is being vertically shifted down $5$ units from $g$.

(c) Find the inverse for $h.$

Note: You should be able to do this by hand first and verify your answer with a technology.